WPS3645 Efficiency of Public Spending in Developing Countries: An Efficiency Frontier Approach1 Santiago Herrera Gaobo Pang Abstract Governments of developing countries typically spend between 15 and 30 percent of GDP. Hence, small changes in the efficiency of public spending could have a major impact on GDP and on the attainment of the government's objectives. The first challenge that stakeholders face is measuring efficiency. This paper attempts such quantification and has two major parts. The first one estimates efficiency as the distance between observed input-output combinations and an efficiency frontier (defined as the maximum attainable output for a given level of inputs). This frontier is estimated for several health and education output indicators by means of the Free Disposable Hull (FDH) and Data Envelopment Analysis (DEA) techniques. Both input-inefficiency (excess input consumption to achieve a level of output) and output-inefficiency (output shortfall for a given level of inputs) are scored in a sample of 140 countries using data from 1996 to 2002. The second part of the paper seeks to verify empirical regularities of the cross- country variation in efficiency. Results show that countries with higher expenditure levels register lower efficiency scores, as well as countries where the wage bill is a larger share of the government's budget. Similarly, countries with higher ratios of public to private financing of the service provision score lower efficiency, as do countries plagued by the HIV/AIDS epidemic and those with higher income inequality. Countries with higher aid-dependency ratios also tend to score lower in efficiency, probably due to the volatility of this type of funding that impedes medium term planning and budgeting. Though no causality may be inferred from this exercise, it points at different factors to understand why some countries might need more resources than others to achieve similar educational and health outcomes. World Bank Policy Research Working Paper 3645, June 2005 The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors, or the countries they represent. Policy Research Working Papers are available online at http://econ.worldbank.org. 1 The paper is a draft of work in progress that carries the names of the authors and should be cited accordingly. The authors thank Antonio Estache, Jorge Garcia, April Harding, Ulrich Lachler, Vikram Nehru, John Rust, and participants at seminars of the Economic Policy and Debt Department of the World Bank., the Banca d'Italia Workshop on Public Finance and the Economics Department at the University of Maryland for helpful comments on earlier drafts of the paper. The dataset, specific-country results, and programs are available in the World Bank PRMED (Economic Policy and Debt Department) website. Table of Contents I. Introduction..........................................................................................1 II. Measuring Efficiency: Methodologies and Overview of the Literature...................1 II.1. Methods for Measuring Efficiency........................................................2 II.2. Overview of Precursor Papers.............................................................5 III. Empirical Results.................................................................................8 III.1. Input and Output Indicators: Description, Assumptions and Limitations..........8 III.2. Single Input-output Results..............................................................12 III.3. Multiple Inputs and Multiple Outputs.................................................20 III.4. Efficiency Change Over Time..........................................................24 IV. Explaining Inefficiency Variation Across Countries......................................25 IV.1. Method, Variables and Data Description.............................................25 IV.2. Results.....................................................................................28 V. Concluding Remarks and Directions for Future Work.....................................31 References............................................................................................36 I. Introduction Governments of developing countries typically spend resources equivalent to between 15 and 30 percent of GDP. Hence, small changes in the efficiency of public spending could have a significant impact on GDP and on the attainment of the government's objectives whichever these are. The first challenge faced by stakeholders is measuring and scoring efficiency. This paper attempts such quantification. Additionally it verifies statistically some empirical regularities that describe the cross country-variation in the estimated efficiency scores. The paper has four chapters following this Introduction. The first one presents the methodology that defines efficiency as the distance from the observed input-output combinations to an efficient frontier. This frontier, defined as the maximum attainable output for a given input level, is estimated using the Free Disposable Hull (FDH) and Data Envelopment Analysis (DEA) techniques. The exercise focuses on health and education expenditure because they absorb the largest share of most countries' budgets, and because of lack of data availability for international comparisons in other types of expenditures. The second chapter estimates the efficiency frontiers for nine education output indicators and four health output indicators, based on a sample of 140 countries and data for 1996- 2002 Both input-efficiency (excess input consumption to achieve a level of output) and output-efficiency (output shortfall for a given level of inputs) are scored. The chapter presents both the single input-single-output and the multiple-inputs multiple-outputs frameworks. In addition, this chapter explores how expenditure efficiency has changed over time. The third chapter seeks to identify empirical regularities that explain cross-country variation in the efficiency scores. Using a Tobit panel approach, this chapter shows that higher expenditure levels are generally associated with lower efficiency scores. Similarly, countries in which the wage bill is a larger share of the total budget tend to have lower efficiency scores. Three other variables that explain the cross country variation in efficiency scores are the degree of urbanization (positively correlated with efficiency, the prevalence of the HIV/AIDS epidemic (negatively associated with efficiency scores), and inequality in income distribution (higher inequality associated with lower efficiency). The fourth and last chapter summarizes the conclusions. II. Measuring Efficiency: Methodologies and Overview of the Literature The object of this chapter is to briefly describe the specific empirical methods applied in this paper to measure efficiency and to survey the literature more directly related to the analysis of public expenditure efficiency. Empirical and theoretical measures of efficiency are based on ratios of observed output levels to the maximum that could have 1 been obtained given the inputs utilized. This maximum constitutes the efficient frontier which will be the benchmark for measuring the relative efficiency of the observations. There are multiple techniques to estimate this frontier, surveyed recently by Murillo- Zamorano (2004), and the methods have been recently applied to examine the efficiency of public spending in several counties. These are the topics of the next two sections. II.1. Methods for Measuring Efficiency. The origin of the modern discussion of efficiency measurement dates back to Farell (1957), who identified two different ways in which productive agents could be inefficient: one, they could use more inputs than technically required to obtain a given level of output, or two, they could use a sub-optimal input combination given the input prices and their marginal productivities. The first type of inefficiency is termed technical inefficiency while the second one is known as allocative inefficiency. These two types of inefficiency can be represented graphically by means of the unit isoquant curve in Figure1. The set of minimum inputs required for a unit of output lies on the isoquant curve YY'. An agent's input-output combination defined by bundle P produces one unit of output using input quantities X1 and X2. Since the same output can be achieved by consuming less of both inputs along the radial back to bundle R, the segment RP represents the inefficiency in resource utilization. The technical efficiency (TE), input-oriented, is therefore defined as TE = OR/OP. Furthermore, the producer could achieve additional cost reduction by choosing a different input combination. The least cost combination of inputs that produces one unit of output is given by point T, where the marginal rate of technical substitution is equal to the input price ratio. To achieve this cost level implicit in the optimal combination of inputs, input use needs to be contracted to bundle S. The input allocative efficiency (AE) is defined as AE = OS/OR. X2/Y Y T P R S Y' O X1/Y Figure 1 Technical and Allocative Inefficiency 2 The focus of this paper is measuring technical efficiency, given the lack of comparable input prices across the countries. This concept of efficiency is narrower than the one implicit in social welfare analysis. That is, countries may be producing the wrong output very efficiently (at low cost). We abstract from this consideration (discussed by Tanzi 2004), focusing on the narrow concept of efficiency. Numerous techniques have been developed over the past decades to tackle the empirical problem of estimating the unknown and unobservable efficient frontier (in this case the isoquant YY"). These may be classified using several taxonomies. The two most widely used catalog methods into parametric or non-parametric, and into stochastic or deterministic. The parametric approach assumes a specific functional form for the relationship between the inputs and the outputs as well as for the inefficiency term incorporated in the deviation of the observed values from the frontier. The non- parametric approach calculates the frontier directly from the data without imposing specific functional restrictions. The first approach is based on econometric methods, while the second one uses mathematical programming techniques. The deterministic approach considers all deviations from the frontier explained by inefficiency, while the stochastic focus considers those deviations a combination of inefficiency and random shocks outside the control of the decision maker. This paper uses non-parametric methods to avoid assuming specific functional forms for the relationship between inputs and outputs or for the inefficiency terms. A companion paper will explore the parametric approach, along the lines proposed by Greene (2003). The remainder of the section briefly describes the two methods: the Free Disposable Hull (FDH) and the Data Envelopment Analysis (DEA) The FDH method imposes the least amount of restrictions on the data, as it only assumes free-disposability of resources. Figure 2 illustrates the single-input single-output case of FDH production possibility frontier. Countries A and B use input XA and XB to produce outputs YA and YB, respectively. The input efficiency score for country B is defined as the quotient XA/XB. The output efficiency score is given by the quotient YB/YA. A score of one implies that the country is on the frontier. An input efficiency score of 0.75 indicates that this particular country uses inputs in excess of the most efficient producer to achieve the same output level. An output efficiency score of 0.75 indicates that the inefficient producer attains 75 percent of the output obtained by the most efficient producer with the same input intake. Multiple input and output efficiency tests can be defined in an analogous way. 3 Output D E C A YA YB B O XA XB Input Figure 2 Free Disposal Hull (FDH) production possibility frontier The second approach, Data Envelopment Analysis (DEA), assumes that linear combinations of the observed input-output bundles are feasible. Hence it assumes convexity of the production set to construct an envelope around the observed combinations. Figure 3 illustrates the single input- single output DEA production possibility frontier. In contrast to the vertical step-ups of FDH frontier, DEA frontier is a piecewise linear locus connecting all the efficient decision-making units (DMU). The feasibility assumption, displayed by the piecewise linearity, implies that the efficiency of C, for instance, is not only ranked against the real performers A and D, called the peers of C in the literature, but also evaluated with a virtual decision maker, V, which employs a weighted collection of A and D inputs to yield a virtual output. DMU C, which would have been considered to be efficient by FDH, is now lying below the variable returns to scale (VRS, further defined below) efficiency frontier, XADF, by DEA ranking. This example shows that FDH tends to assign efficiency to more DMUs than DEA does. The input-oriented technical efficiency of C is now defined by TE = YV/YC. CRS F D Output N VRS Y V C A B VRS O X Input Figure 3 DEA production possibility frontier 4 If constant returns to scale (CRS) characterize the production set, the frontier may be represented by a ray extending from the origin through the efficient DMU (ray OA). By this standard, only A would be rated efficient. The important feature of the XADF frontier is that this frontier reflects variable returns to scale. The segment XA reflects locally increasing returns to scale (IRS), that is, an increase in the inputs results in a greater than proportionate increase in output. Segments AD and DF reflect decreasing returns to scale. It is worth noticing that constant returns to scale technical efficiency (CRSTE) is equal to the product of variable returns to scale technical efficiency (VRSTE) and scale efficiency (SE). Accordingly, DMU D is technically efficient but scale inefficient, while DMU C is neither technically efficient nor scale efficient. The scale efficiency of C is calculated as YN/YV. For more detailed exploration of returns to scale, readers are referred to Charnes, Cooper, and Rhodes (1978) and Banker, Charnes, and Cooper (1984), among others.2 The limitations of the non-parametric method derive mostly from the sensitivity of the results to sampling variability, to the quality of the data and to the presence of outliers. This has led recent literature to explore the relationship between statistical analysis and non-parametric methods (Simar and Wilson, 2000). Some solutions have been advanced. For instance, confidence intervals for the efficiency scores can be estimated using asymptotic theory in the single input case (for input-efficiency estimators) or single- output (in the output efficiency) case, given these are shown to be maximum likelihood estimators (Banker, 1993 and Goskpoff, 1996). For multiple input-output cases the distribution of the efficiency estimators is unknown or quite complicated and analysts recommend constructing the empirical distribution of the scores by means of bootstrapping methods (Simar and Wilson, 2000). Other solutions to the outlier or noisy data consist in constructing a frontier that does not envelop all the data point, building an expected minimum input function or expected maximum output functions (Cazals, Florens and Simar, 2002, and Wheelock and Wilson, 2003). Another limitation of the method, at least in the context in which we will apply it, is the inadequate treatment of dynamics, given the lag between input consumption (public expenditure) and output production (health and education outcomes). II.2. Overview of Precursor Papers There is abundant literature measuring productive efficiency of diverse types of decision making units. For instance, there are papers measuring efficiency of museums (Bishop and Brand, 2003), container terminals (Cullinane and Song, 2003), electric generation plants (Cherchye and Post 2001), banks (Wheelock and Wilson, 2003), schools (Worthington, 2001) and hospitals (Bergess and Wilson, 1998), among others. Few papers, however, analyze aggregate public sector spending efficiency using cross-country data. These are the direct precursors of this paper and are the focus of this section's survey. 2 The technical Appendix D provides more detailed exploration of the Data Envelopment Analysis, which shows how the peers are identified, how the virtual DMUs are constructed, and how weights to the different efficient DMUs and efficiency scores are calculated. 5 Gupta and Verhoeven (2001) employ the input-oriented FDH approach to assess the efficiency of government spending on education and health in 37 African countries in 1984-1995. Using several output indicators for health and education, they construct efficiency frontiers for each of the indicators and for each of the time periods they considered. That is, they used a single input-single output for each time period. They find that, on average, African countries are inefficient in providing education and health services relative to both Asian and the Western Hemisphere counties. They also report, however, an increase in the productivity of spending through time, as they document outward shifts in the efficiency frontier. Finally the authors report a negative relationship between the input efficiency scores and the level of public spending, which leads them to conclude that higher educational attainment and health output requires efficiency improvement more than increased budgetary allocations. Evans and Tandon (2000) adopt a parametric approach to measure efficiency of national health systems for the World Health Organization, by estimating a fixed effects panel of 191 countries for the period 1993-1997. Health output was measured by the disability adjusted life expectancy (DALE) index, while health expenditures (public and private aggregated) and the average years of schooling of the adult population were considered as inputs. The output-efficiency score is defined as the ratio of actual performance above the potential maximum. The authors also introduce the square of the inputs (average years of schooling and expenditure), arguing it's a second-order Taylor-series approximation to an unknown functional form. The fact that the quadratic terms are significant may be an indication of the importance of non-linearity, but may also reflect neglected dynamics or heterogeneity in the sample (Haque, Pesaran and Sharma, 1999), given that both developed and developing nations were included. An interesting contribution of the paper is a construction of a confidence interval for the efficiency estimates through a Monte-Carlo procedure. These authors document a positive relationship between their efficiency scores and the level of spending. The more efficient health systems are those of Oman, Chile and Costa Rica. The more inefficient countries are all African: Zimabawe, Zambia, Namibia, Botswana, Malawi and Lesotho. Jarasuriya and Woodon (2002) also adopt a parametric approach to estimate efficiency of health and education provision in a sample of developing countries. The authors estimate the efficiency frontier by econometric methods. These authors consider separately an educational attainment indicator (net primary enrollment) and a health output indicator (life expectancy) and estimate a functional linear relationship between these output indicators and three inputs: per capita GDP, spending per-capita, and the adult literacy rate. Using a panel of 76 countries for the period 1990 to 1998, they found no relationship between expenditure and the educational or health output variables when they include the per-capita GDP. This led the authors to conclude that spending more is not a guarantee to obtain better education or health results. The authors do not point at the correlation between the two variables as a possible cause of this problem, which we discuss in the next section. The countries with the lowest efficiency in health indicators are all African (Malawi, Zambia, Mozambique, Ethiopia) as well as in education attainment (Ethiopia, Niger, Burkina Faso). 6 The authors go further by attempting to explain the cross-country variation in efficiency and find that the degree of urbanization and the quality of bureaucracy are the most relevant variables. To capture possible non-linearity, the authors introduce these variables squared. This stage of their work poses several problems. First, it is possible that the (non-linear) quadratic terms reflect heterogeneity across countries and dynamics across time. As shown by Haque, Pesaran, and Sharma (1999), this would produce inconsistent estimates. Second, the authors do not adjust for the fact that the dependent variable (efficiency scores) is censored, given that it can adopt only values between zero and one. And third, the authors do not consider the serial correlation of the efficiency scores (Simar and Wilson, 2004) Greene (2003a) combines the previous two papers in the sense he concentrated on health efficiency only using the WHO panel data and explained inefficiency scores variation across the sample of counties. Greene's stochastic frontier estimation is much more general and flexible, as it allows for time variation of the coefficients and heterogeneity in the countries' sensitivity to the explanatory variables. The author first estimates a health production function using expenditure (public and private together) and education as inputs, and then explains inefficiency with a set of explanatory variables of which the only significant ones are the income inequality measure, GDP per capita and a dummy variable for tropical location. Afonso, Schuknecht and Tanzi (2003) examine the efficiency of public spending using a non-parametric approach. First, they construct composite indicators of public sector performance for 23 OECD countries, using variables that capture quality of administrative functions, educational and health attainment, and the quality of infrastructure. Taking the performance indicator as the output, and total public spending as the input, they perform single-input, single-output FDH to rank the expenditure efficiency of the sample. Their results show that countries with small public sectors exhibit the highest overall performance. Afonso and St. Aubyn (2004) address the efficiency of expenditure in education and health for a sample of OECD countries applying both DEA and FDH. This paper presents detailed results by comparing input-oriented and output-oriented efficiency measurements. The small overlap of the samples limits the comparability of these results with those presented in the next section. An apparently strange result, reported in earlier drafts of the paper, was the inclusion of Mexico as one of the benchmark countries (on the efficiency frontier). The result is strange given that the sample is the OECD countries, and it counterintuitive. This is the result of Mexico having very low spending and low education attainment results, hence it cam be considered as the "origin" of the efficiency frontier. The next chapter discusses this topic and reports similar counterintuitive results but for other countries. 7 III. Empirical Results III.1. Input and Output Indicators: Description, Assumptions and Limitations Cross-country comparisons assume some homogeneity across the world in the production technology of health and education.3 There are two particular aspects in which the homogeneity assumption is important. First, the comparison assumes that there is a small number of factors of production that are the same across countries. Any omission of an important factor will yield as a result a high efficiency ranking of the country that uses more of the omitted input. Second, the comparison requires that the quality of the inputs is more or less the same, with the efficiency scores biased in favor of countries where the quality is of higher grade. Factor heterogeneity will not be a problem, as long as it is evenly distributed across countries. It will be problematic if there are differences between countries in the average quality of a factor (Farrell, 1957). The exercise that we present suffers from this limitation, given that the main input in both production technologies is used more intensively in richer countries (with higher per-capita GDP). The main input is public spending per capita on education and health measured in constant 1995 US dollars in PPP terms. A clear positive association between this variable and per-capita GDP can be verified (Figures 4 and 5). This positive association between expenditure and the level of economic development (as measured by per-capita-GDP) may be explained by several reasons.. One of them could be the Balassa-Samuelson effect, according to which price levels in wealthier countries tend to be higher than in poorer countries. This applies to both final goods and factor 4 prices. Thus price of the same service (health or education, for instance) will be higher in the country with higher GDP. Similarly, wages in the relatively richer counties are higher, given the higher marginal productivity of labor, which will tend to increase costs, especially in labor-intensive activities as health and education. Figure 4 can be interpreted as evidence of the validity of Wagner's hypothesis at the cross-country level. This hypothesis, postulates that there is a tendency for governments to increase their activities as economic activity increases. Since 1890 Wagner postulated that economic development implied rising complexities that required more governmental activity, or that the elasticity of demand for publicly provided services, in particular education was greater than one. This hypothesis has been tested econometrically (Chang, 2002) in time series and cross-country settings, showing that this is nothing particular of the series used for the present study. 3See Table B.5 in Appendix B for the list of countries included in the study. 4 The Balassa-Samuelson effect refers to the fact that price levels are higher in richer countries than in poorer countries. It can be shown that relative wages and relative prices are a function of the marginal productivity of labor in the traded goods. Given higher capital abundance in the richer countries, the productivity of labor tends to be higher in these countries, and hence will be wages and prices. 8 Education Spending vs GDP per capita Health Spending vs GDP per capita 8 8 SAUBRB KWT CZESVN MA C HRV SVK HUN ARE 6 NAMBWA ZAF ES T MYPOL S ARG BRB SVK KNA HUN ARGCZEBHS OMNKOR BHR 6 SAU BHRBHS KWT onitci VCTTON LCATUN URY MECHL LTU HRV ARE CRIPOLT LTUES ZWE MKD ZAF KNA GRD X ATG NAM PAN TUN ATG OMNKOR SGP LSO VUTJAMJORBLRBLZTUR GAB DMACOLBW ROMRUS GUYPRY SWZFJIDMACOLBRATTO IRNTHA LVACRIMUS CPV WSMROM DZAPANRUS URY MKD BGRLVAMECHL BRA X BGR GUY ed SYRPHLKAZ MARUKRPER BLRVCTTON WSMVENGRD BOL DOM GNQ JORSLVDZA UKRPRY CPVFJILCA IRNTHA TTOS MYMUS GNQ LBN SLV onitcide ZWE PER BLZ GAB DOM pr MDASDN UZB TGOMRTSLBNIC MNG HND AZE TKM JAMSWZ IND pr DJILSOHND SLBNIC ALBLBN KAZ ARM BOL PNG 4 LKACHN ECUGTM YEM KEN SENGMB CIV COMGHA ARM DJI MNG VUT CHN SYR LKA EGYPHL KGZ AGO PNG GTM 4 MAR earnLi CMR MDA NP LBGD GEO PA K VNM GMBGHA MRT GIN IDN SENHTI UZB GIN MWIETH ERI BENRWA UGA LAOKHM MOZ RWA ERI KGZCOMAGO TGO VNM BDI UGA NERTCD TJK MLIMOZ ZMB MDG CAF GNB BFACAFNPLLAOKHM GEO IND GNB earni/L ZMB TCDKEN COG BGD PA K IDN BFA MWI BEN CIVCMR AZE du/el TZA 2 eahl NER MLIZAR YEM MDG SDN 2 SLE TZABDI ETHTJK SLE NGA COG 0 0 6 7 8 9 10 6 7 8 9 10 lgdp lgdp ledu Linear prediction lhea Linear prediction Figure 4. Public Expenditure and GDP (both per capita and in logs) Previous studies that measured the efficiency of public spending recognized the positive association and suggested alternative solutions. One possibility is to split the sample by groups of countries (Gupta and Verhoeven, 2001). We follow this approach by excluding the industrialized nations from the sample, and by presenting most of the results clustered regionally (Africa (AFR), East Asia and Pacific(EAP), Latin America and Caribbean (LAC), Middle-East and North Africa (MNA) and South Asia (SAS)). A second alternative incorporates directly the per-capita GDP as a factor of production, jointly with expenditure and other inputs (Jarasuriya and Woodon 2002). The problem with this approach is that it combines variables derived from a production function approach, and hence with clear interpretation, with others (GDP per capita) that are difficult to interpret from any viewpoint. When the two types of variables are combined, their effects cannot be disentangled. A third option consists in using as an input the orthogonal component of public expenditure to GDP5. We scored the efficiency using as input both the original expenditure variable and the orthogonalized variable. The goodness-of-fit of each model was gauged based on the frequency distribution of the inefficiency measures, as suggested by. Farrell (1957) and Varian (1990). Comparing the efficiency distributions (Figures 5) it is clear that the orthogonalized expenditure version produces distributions that are not skewed towards extreme inefficient outcomes. On this basis, the paper considered the orthogonal component of expenditure on health and education. 5The orthogonalized expenditure variable is the residual of the linear regression between pubic expenditure and GDP per capita. Since residuals may take positive and negative values, the variable was right-shifted to avoid negative values to facilitate graphical presentation of the frontiers. 9 FDH FDH 8 15 6 10 ytisn yti 4 De ensD 5 2 0 0 0 .2 .4 .6 .8 1 .4 .6 .8 1 score score Unorthogonalized Public Expenditure Orthogonalized Public Expenditure Figure 5. Density of Efficiency Scores ­ Gross Primary School Enrollment This paper uses nine indicators of education output and four indicators of health output. 6 The education indicators are: primary school enrollment (gross and net), secondary school enrollment (gross and net), literacy of youth, average years of school, first level complete, second level complete, and learning scores. Though the ideal educational output indicator are comparable learning scores, international assessments are based on samples mostly composed of developed nations, limiting the applicability to the present paper. However, Crouch and Fasih (2004) recently combined several international assessments to obtain a larger sample of comparable results.7 Unfortunately they only do it for one period. The correlation between the learning scores and other output variables is high (.81 with net secondary school enrollment and .76 with average years of school), as shown in Figure 68. The health output indicators are: life expectancy at birth, immunization (DPT9 and measles), and the disability-adjusted life expectancy (DALE). The cross-country comparisons with this set of indicators assume some form of data homogeneity, which might be problematic given the diversity of counties in the sample considered. Even for a more homogeneous group of countries, such as the OECD, there is call for caution when comparing expenditure levels in member countries (Jounard, 6 The data sources are: the World Bank World Development Indicators (WDI), Barro-Lee database, and Crouch and Fasih (2004) the World Health Organization (Mathers et al, 2000).A complete list of variables and data sources can be found in Table B.6 of Appendix B. 7 Crouch and Fasih (2004) consider several international tests of learning achievement in math, science and literacy applied at different levels of the school system. The tests are the following: TIMSS (Third International Mathematics and Science Survey), PIRLS (Progress in International Literacy Study), PISA (program for International Student assessment), Reading Literacy Study, LLECE (Laboratorio Since the tests have different samples, they converted all test scores through iterative comparisons to a single numeraire.Latinoamericano de Evaluaciond ela Calidad de la Educacion, SACMEQ (Southern Africa Consortium for Monitoring of Education Quality), MLA (Monitoring Learning Achievement) 8 The correlation coefficients and Figure 6 exclude developed nations for the Crouch and Fasih (2004) sample. 9 DPT is Diphtheria-Pertussis and Tetanus 10 et.al. 2003). There is very little to do to overcome this limitation, except subdivide the sample into different groups. Probably a regional aggregation can be useful, but even at that level there may be extreme heterogeneity. Correlation: Learning Scores and Net Secondary Enrollment Correlation: Learning Scores and Average Years of School 0 60 600 SGP TWN KOR KOR HKG SVK HUN HUN CZESVN SV N SVK CZE 0 BGR 0 BGR MYS LVA POL MYS POL 50 CUB LTU 50 CUB THA se ROM MDA ROM MEX TTO MKD es MEX TTO orcS TUR TUN BRATUR TUN IRN J OR BRAALB IRN ARG JOR ARG 0 IDN IDN PRY BOLCHL 0 PRY CHL 40 DOM COL PER KWT ng VUT nir SYC orcSgnni 40 HNDCOLBOL DOM KWT PER KEN PHL MUS PHL eaL ar TZA MAR ZWE BLZMUS KEN TZA ZWE 0 MOZ MDG SWZ Le 0 MOZ CMR SWZ UGA 30 BWA 30 BWA BFA ZAF ZAF LSO NAM MLI SEN LSO ZMB 0 0 MWI 20 20 NE R NER 0 20 40 60 80 100 0 2 4 6 8 10 Net Secondary Enrollment Average Years of School Data Source: World Bank WDI & Crouch and Fasih (2004) Data Source: World Bank WDI & Crouch and Fasih (2004) Figure 6. Correlation between Learnings Scores and Other Education Indicators Other four limitations of the analysis arising from the particular data sources are: First, the level of aggregation. The paper uses aggregate public spending on health and education, while using disaggregate measures of output, such as. primary enrollment or secondary enrollment. Ideally, the input should be use separately public spending in primary and secondary education. Similarly, health care spending could be disaggregated into primary care level care and secondary level. The data can be disaggregated even further, by analyzing efficiency at the school or hospital levels. Second, there are omitted factors of production. This is especially true in education, as the paper did not consider private spending due to data constraints for developing nations. If this factor were used more intensively in a particular group of countries, then the efficiency scores (reported in the next section) would be biased favoring efficiency in that group. The third limitation arising from the data is the combination of monetary and non- monetary factors of production. The paper uses together with public expenditure, other non-monetary factors of production such as the ratio of teachers to students, in the case of education, or literacy of adults in the case of health and education. Other factors of production that could have been used were the physical number of teaching hours (in education) or the number of doctors or in-patient beds, as Afonso and St. Aubyn did for the OECD countries. However, inexistent data for a large number of developing countries constrained the options. A fourth limitation arising from the selected indicators, is that these don't allow for a good differentiation between outputs and outcomes. For instance, most of the indicators of education, such as completion and enrollment rates do not measure how much learning is taking place in a particular country. In education, this paper advances by considering the learning scores as one of the indicators. In health, other outcomes such as the number 11 of sick-day leaves or the number of missed-school days because of health-related causes could be better reflections of outcomes. Two of the selected health output indicators, DPT and measles immunization are delivered in vertical programs, that is, in campaigns that are relatively independent of basic health systems and therefore may not be good indicators of the actual quality of the health system. Finally, the fact that life expectancy is influenced by diet, lifestyle, and a clean environment, that to the extent that are not included as factors of production may bias the efficiency scores. III.2. Single Input-output Results III.2.1. FDH and DEA analysis: Education Figures 7a-c show both FDH and DEA estimation of the efficiency frontier for three of the nine output indicators: gross primary school enrollment, first level complete and learning scores. Individual country efficiency scores for the three indicators are reported in Table B.1-3 of Appendix B10. The graphical efficiency frontiers for other output indicators can be found in Appendix B (Figure B.1). Figure 7.d illustrates the efficiency frontier for the learning scores if the developed countries are included in the sample, demonstrating the sensitivity of the results to the sample definition. This fact is particularly acute in the case of learning scores which capture the quality of education dimension that no other indicator captures. While in the sample of developing countries Chile, Hungary and the Czech Republic are on the frontier; once the developed nations are included they appear as inefficient. The complete set of efficiency scores (including and excluding the set of developed countries can be found in Table B.2 and B.3 in Appendix B11 10The efficiency scores of all the indicators can be found at the PRMED website indicated in footnote 1. 11The frontier depicted in Figure 7.d. excludes Japan, Korea, Ireland and Belgium to facilitate comparisons with the frontier without developed nations. 12 Free Disposable Hull (FDH) Data Envelopment Analysis (DEA) Gross Primary Enrollment vs Education Expenditure Gross Primary Enrollment vs Education Expenditure 0 0 14 BRA 14 BRA GAB MWIV CP GAB MWIV CP ent PER UGA TGO ent 0 PER UGA TGO mlol 120 CH N BLZ ARG KNA BLZ CHN FJI ml 12 ARG KNA FJI PHL NPL NA M DOM PHL NPL NA M RWA LSOTUN ZAF DOM LCA ol RUSLAO COL RWA GUYBOL MEX PRY TON LSOTUNZAF LCA URY IDN RUSLAO COLGUYBOL MEX PRY TON URY IDN L KA nrEl L KA VNM PAN L BN KHMMUSHND VNM PAN BL R SWZ VUT SLV L BN KHMMUSHND DZACRI BL RSWZ VUT 0 SLV SYR DZACRI SYR BWA BRB TJK ZWE BWA BR B 0 ROMOKGZNICSVK TJK CZEHUN ZWE MAC BHR BGRCHLTT ROMOKGZ MDGWSMLTU NICSVK CZEHUN VCT MAC BHR BGRCHLTT VCT IND ES T TUR AZESLB MDGWSMLTU MKD IN D MKD nrEl 10 J AM DMA POL LVA MYS ES T 10 J AM DMAPOL LVA MYS BH S GTM KORBGD TUR AZE hoocS GEOKAZHRV SLB BHS GTM KORBGD MAR IRN ARM CMR GRDMNGTHAJOR MAR IRN GEOKAZHRV ARM CMR KENUZB KWT BE N KENUZB KWT BE N MDA MDA OMNCOGZMBUK R MOZ MRT OMNCOGZMBUK R MOZ MRT hoocS GRDMNGTHAJOR y COM 80 COM y GMB GHA 80 PNG GMB GHA ar PN G YEM CIV YEM ar CIV mirPssorG PAKGNB SE N SAU SAU AGOTZA CAF TCD SLE mirP PAKGNBSE N AGO CAFTZA TCD SLE GIN GIN 60 s 60 ERI BDI ERI BD I SDN SDN ETH osr ETH MLI MLI G BFA BFA 40 40 DJI DJI NER NER 300 400 500 600 700 800 300 400 500 600 700 800 Orthogonalized Public Expditure on Education Orthogonalized Public Expditure on Education Data Source: World Bank WDI Data Source: World Bank WDI (a.1) (a.2) First Level Complete vs Education Expenditure First Level Complete vs Education Expenditure TUR TUR 40 40 )+ )+ 51 51 gea( 30 POL BGR age( 30 POL BGR ARG ARG THA THA teelp MYS teelp MYS FJI PNG PRY BWA 20 PNG PRY BWA HUN PAN ComleveLtsriF HUN PAN IDN IDN ME X PHL ME X HR SYR HR V SYR V JAM JAM GUY HND CRI CHN BOL LKABRA GUY CHN BOL KOR TTOSVK LKABRA TUN BRB KOR TTOSVK HND CRI SLV MWI KEN LSO MWI TUN LSO BRB URY CZE INDZMBDZA SWZ ZAF 10 URY SLV KEN 10 UGATZA GTMCHL CZE CMR INDZMBDZA GTMCHL CMRRWA COLNI C ZWE COLNICRWA UGATZA SWZ ZAF ZWE DOM PAK BGD SENIRN JOR DOM BGD ROM PER COG ROM PER PAK COG CAFMOZTGO SENIRN JOR moCleveLtsriF FJI 20 PHL CAFMOZTGO GHA GHA MUS NP L BEN SDN MUS NP L BEN SDN GA B SL E GA B SL E GNB NER MLI KWT GNB NER MLI KWT 0 0 0 100 200 300 400 0 100 200 300 400 Orthogonalized Public Expditure on Education Orthogonalized Public Expditure on Education Data Source: World Bank WDI Daat Source: World Bank WDI, Barro-Lee database (b.1) (b.2) Learning Scores vs Education Expenditure Learning Scores vs Education Expenditure 600 600 HUN SV K HUN RUS CZE SV K RUS CZE 0 BGR BGR POL LVAMYS POL LVAMYS 50 500 LTU LTU ROM THA ROM THA MDA MDA es TTO MKD MEX es TTO MKD MEX JOR orcSgnni TUN TURARG JOR TUN TURARG IRN BRA IRN BRA 0 IDN IDN CHL PRY BOL orcS CHL COL PRY HND BOL KWT 40 PER COL HND KWT 400 PER VUT ng VUT ni PHL KEN ar MUS PHL KEN MUS BLZ TZAMAR BLZ ZWE ZWE CMR TZAMAR Le MOZ SWZ 0 CMR MOZ UGA MDG SWZ Lear UGA MDG 30 300 BWA BWA BFA BFA CIV CIV ZAF ZAF ZMB MLI LSO NAM ZMB MLI LSO NAM SEN 0 SEN MWI MWI 20 200 NE R NE R 0 100 200 300 400 0 100 200 300 400 Orthogonalized Public Expditure on Education Orthogonalized Public Expditure on Education Data Source: World Bank WDI & Crouch and Fasih (2004) Data Source: World Bank WDI & Crouch and Fasih (2004) (c.1) (c.2) 13 Learning Scores vs Education Expenditure Learning Scores vs Education Expenditure 0 60 600 NLDSVKHUN AUS NLDSVKHUN CZE RUS CA N CH E AUT FIN SW E AUS CZE RUS CA N CHE AUT FIN SW E 0 GBR DE U FRA GBR DE UBGRUSA FRA ESPBGRUSA POLLMYS VA ESP POLLMYS VA ISLNZL NOR 50 ISLNZL NOR GRC 500 GRC DNK ITA DNK ITA LTUTHA PRT ROM LTUTHA PRT ROM se MDACY P IS R MDACY P IS R TTOMEX MKD es TTOMEX MKD JOR orcS ARG TUR IRN TUN ID BRA ARG TUR IR N JOR TUN IDN BRA N CHL COLPRYBOL orcS CHL DOM COLPRYBOL HND KWT gn 400 DOM PER HND KWT 400 PER VUT gn VUT nir ni PHL KEN MUS PHL KEN MUS MAR BLZ MAR BLZ ZWE ZWE CMRTZA Lea MOZSWZ 0 CMR TZA MOZSWZ MDG MD G Lear UGA UGA 30 300 BWA BWA BFA BFA CIV CIV ZAF ZAF ZMB MLI LSO NAM ZMB MLI SEN SEN LSO NAM MWI MWI 200 200 NER NER 600 800 1000 1200 1400 1600 600 800 1000 1200 1400 1600 Orthogonalized Public Expditure on Education Orthogonalized Public Expditure on Education Data Source: World Bank WDI & Crouch and Fasih (2004) Data Source: World Bank WDI & Crouch and Fasih (2004) (d.1) (d.2) Figure 7 Education Efficiency Frontier: Single Input and Single Output Several results may be highlighted: a. In general, the rankings are robust to the output indicator selected. This can be can be verified by the Spearman rank-correlation coefficient (see Tables C.1 and C.2 in Appendix C), that are all positive, significant and high. The range oscillates from a minimum of .53 to a maximum of .94, with the mean of .70. This result implies that countries appearing as efficient (or inefficient) according to one indicator, are ranked similarly when other output indicator is used. b. Despite the orthogonalization by GDP, the relatively rich countries tend to be in the less efficient group, i.e. countries with higher per-capita GDP spend more than other countries in attaining similar education outcomes. Higher spending may reflect the higher cost of tertiary education. This is one factor that may help explain the stand-out of Estonia, Latvia, and Poland. Oil-rich countries, such as Kuwait and Saudi Arabia, tend to be in the group of relatively more inefficient producers. c. Another group of relatively inefficient producers are those with "average" expenditure levels but extremely low education attainment. Among those are mostly African counties (Angola, Niger, Burkina Faso, Sudan, and Ethiopia), some Middle Eastern countries (Djibouti, and Yemen) and South Asia (Bangladesh and Pakistan). Table B.1-3 in Appendix B list the output-efficiency scores for three of the indicators. d. Output-efficiency rankings also vary with the selected output indicators. The spearman correlation coefficient of the output-efficiency scores (see Tables C.3 and C.4 in Appendix) show that these are robust to the selected indicator, though the mean of the correlation coefficients is lower (.52) and the range is somewhat higher (.30 to .95) than those registered in the input-efficiency rankings. e. In an attempt to identify clusters of more efficient countries and more inefficient countries, the top (and bottom) 10 percent of the efficiency ranking were selected for each of the indicators. If a country appeared in the efficient (inefficient) tail in three or more of the indicators, it was included in Table 1. 14 Table 1. Education Attainment: Single Input, Single Output Input-Efficient Output Efficient More efficient Uruguay, Korea, Dominican Uruguay, Korea, Bahrain, Republic, Indonesia, Bahamas Guatemala, China, Bahamas, Bahrain, El Salvador Least efficient Botswana, South Africa, Niger, Mali, Tanzania, Kuwait, Tunisia, Lesotho, Burkina Fasso, Gunea-Bissau, Barbados, Saudi Arabia, Ethiopia, Guinea, Burundi, Zimbawe, Namibia, Malaysia, Sudan, Sierra Leone, Chad St, Lucia, Jamaica, St, Vincent, Latvia, f. This clustering exercise reveals (Table 1) a group of African countries as the most inefficient. Two oil-rich countries are included in this group as well. Among the more efficient group of countries we consistently find Uruguay, Korea, Bahamas, and Bahrain. Explaining why these particular sets of countries appear in each cluster requires more in-depth analysis. The last section of this paper attempts to associate efficiency results with some explanatory variables. g. To grasp the order of magnitudes of the deviations from the efficiency frontier, we computed an average for all indicators for the inefficient countries. The input- efficiency estimations indicate that the most inefficient decile could reach the same educational attainment levels by spending approximately 50 percent less. The output efficiency estimators indicate that, on average, with the expenditure level this group could reach educational attainment levels four times as high. h. It is critical to note that even if a country appears as efficient, there might still be a significant discrepancy between the observed output level and the desired or target output level. For instance, Bahamas, Bahrain, Dominican Republic and Guatemala appear as efficient countries on the efficiency frontier or very close to it (Figure 7 a.1). However, these countries are still far away from where Gabon or Brazil are, and could consider desirable to achieve those target enrollment rates. Both Guatemala and Dominican Republic spend two percent of GDP on education but have (net) secondary enrollment rates below 40 percent. And net primary enrollment is about 80 percent. It would be difficult to argue that that is a desirable outcome, though it is an efficient one. Similarly, though Chile appears as efficient with learning scores of about 400, the country could still achieve higher learning scores of over 500 points at the cost of additional public spending. The important thing is that the country moves along the efficiency frontier to the higher target output level. Countries can even improve efficiency by exploiting scale economies if they are operating in the increasing returns to scale zone of the production possibility frontier (output levels smaller than that of point A, Figure 3) i. The regional aggregation of the efficiency scores by each individual output indicator shows that scores are lower when they are input oriented (Table 2) than 15 when they are output oriented (Table 3).12This is especially true for ECA. In general, we observe higher efficiency scores when primary enrollment is considered as the output indicator. Scores are lower for secondary enrollment, especially when output-oriented measures are considered. Africa and MNA have similar levels of input-inefficiency: in most cases, both regions use public spending in excess of 35 percent than the benchmark cases. EAP, ECA, LAC and SAS spend in excess between 20-30 percent of the benchmark level. The output efficiency scores are lower in Africa Table 2. Educational Attainment: Input-Efficiency scores by regions across the world - Single Input, Single Output AFR EAP ECA LAC MNA SAS Gross primary enrollment .69 .74 .67 .74 .65 .75 Net primary enrollment .68 .78 .72 .77 .68 .71 Gross Secondary enrollment .65 .69 .67 .69 .63 .70 Net secondary enrollment .64 .71 .71 .69 .64 .72 Average years of school .21 .36 .37 .32 .18 .25 First level complete .21 .43 .48 .36 .20 .26 Second level complete .22 .37 .33 .32 .19 .27 Literacy of youth .66 .73 .86 .72 .63 .72 Table 3. Educational Attainment: Output-Efficiency scores by regions across the world - Single Input-Single Output AFR EAP ECA LAC MNA SAS Gross primary enrollment .62 .79 .72 .82 .67 .72 Net primary enrollment .64 .93 .90 .93 .79 .78 Gross Secondary enrollment .23 .50 .70 .61 .54 .39 Net secondary enrollment .26 .58 .84 .66 .60 .44 Average years of school .32 .63 .79 .60 .53 .38 First level complete .19 .49 .50 .36 .22 .20 Second level complete .09 .37 .38 .24 .26 .22 Literacy of youth .72 .95 .99 .94 .88 .66 12The regional aggregation is for illustrative purposes only and was computed as the simple average of the individual country scores obtained for the whole sample. The scores were not computed by constructing separate efficiency frontiers for each region. Hence, they do not reflect the heterogeneity in the individual country scores and possibly do not reflect adequately variations across regions. 16 III.2.2. FDH and DEA Analysis: Health This section considers the case of one input (public expenditure on health per capita in PPP terms) and four alternative output indicators: life expectancy at birth, DPT immunization, measles immunization, and the disability adjusted life expectancy (DALE) index which takes into account both mortality and illness. The efficiency frontiers for each indicator are computed using both the FDH and DEA methodologies. Figures 8a-d show the efficiency frontier for one indicator. The specific country rankings for two of the health indicators are listed in Table B.4 of Appendix B. Free Disposable Hull (FDH) Data Envelopment Analysis (DEA) Life Expectancy vs Health Expenditure Life Expectancy vs Health Expenditure 80 80 CRI KWT CRI KWT ARE CHL ATGJ AM DMABRB ARE CHL AM DMABRB PAN CZE SVN ATGJ PAN CZE SVN URY KOR OMN URY KOR OMN MYS TTO MEXBLZGEOVEN BHRALB LKA GRDSAU ARMVCT POL MEXBLZGEOVEN BHRALB LKA GRDSAU ARMVCT POL ARGSVK HRV TUN MKD ARGSVK HRV MYS TTO LCA TUN MKD MUS LCA BGR JOR LTU HUN MUS JOR LTU LBNPRY KNA TONCOL BGR HUN htriB 70 EST BHSCHNDZA SLV TUR LVA EST THAPHL BHSCHN LBNPRY KNA DZA TONCOL 70 FJIVNMCPV SY R ECU SLVLVA SMROM THAPHL FJIVNMCPV PER SY R ECU SMROM BLR DOMMAR IRNEGYVUTUKR PER BRAUZB TJKNICSLBW TUR BLR BRAUZB IDN AZE KGZ HNDMDA RUS htriB DOMMAR IRNEGYVUTUKR TJKNICSLBW IDN AZE KGZ HNDMDA RUS GTM TKM MNG TKM MNG at KA Z GTM KA Z at y INDPAK BOL GUY y INDPAK BOL GUY BGD COM BGD COM anctc 60 60 NPL ncat NPL SDNGHAPNG SDNGHAPNG YEM YEM pexE KHMBEN MDG KHMBEN MDG LAOGMB GA B LAOGMB HTI SEN pecxE GA B HTI SEN COG fe 50 CMR MRTERI COG TGO ZAF 50 CMR MRTERI TGO ZAF Li SWZ TCD SWZ TCD NAM AGO NGA KE N NAM feiL AGO NGA KE N CIV ZAR GIN DJI CIV ZAR GIN DJI NER TZA BFA TZA NER GNB CAF BFA GNB CAF UGA ETH MLIMOZ UGA ETH MLIMOZ BDI LSO BDI LSO RWA BWAZWE 40 RWA BWAZWE 40 ZMB MWI ZMB MWI SLE SLE 300 400 500 600 700 800 300 400 500 600 700 800 Orthogonalized Public Expditure on Health Orthogonalized Public Expditure on Health Daat Source: World Bank WDI Daat Source: World Bank WDI (a.1) (a.2) Immunization DPT vs Health Expenditure Immunization DPT vs Health Expenditure 0 0 10 OMN ATGUKR W SMROM DMA BLR SVKHUN 10 OMN KNAATGUKR BLR SVKHUN THACHLLKA KWTAZE MEXKA ALB IRNKNA BHRZ KGZBWA UZBTKMVCT POL CZE KWTAZE MEXKA ALB IRNLKA BHRZ KGZBWA UZBTKMVCTW SM DMAROM POL CZE MYS TON LVA HNDMDA JOR TUN TON LVA HNDMDA JOR ARE MARSY EGY R SLV SAU ESTMKD MYS BHS LBNVNMGRDBGR MARSY R SAU TUNPAN ESTMKD GMB MNG LTUPAN HRV SVN ARE THACHLEGY SLV GMBMNG LTU HRV SVN TT O BHS LBNVNMGRDBGR TT O URY FJI PER RUS FJI PER RUS URY KORMUS BLZDZABRAARM NIC NIC CHN BRB CRI KORMUS BRB CRI LCA J AM BLZDZABRAJARM CHN AM ECU GUY LCA GUY MWI ECU RWA LSO MWI 80 SWZBGD GEO VUT CPV TJKTUR RWA LSO KETZA N ERI ARG 80 SWZBGD GEO VUT CPV TJKN KETZA TUR ERI ARG TPD PHLGTM ZMBSLB GHA COL ZAFZWE ZMBSLB GHA COL ZAFZWE IDN PRYBEN NPLBDI IDN BDI NAM PRYBEN NPL NAM DOM COMBOL TPD PHLGTM DOM COMBOL ontiazinu YEM YEM IND VEN 60 CIV MOZ 60 CIV MOZ PAKTGOUGA SEN ontiaz IND VEN PAKTGO UGA SEN LAOMDGPNG LAOMDG PNG KHM niu KHM m CMR ETH MLI GNB m MLI GNB SDN GIN CMR ETH Im GA B MRT GA B SLE CAF SLE mI SDN GIN HTI MRT CAF HTI 40 BFA DJI 40 BFA DJI AGO AGO COG COG NGA ZAR NGA ZAR NER TCD NER TCD 20 20 300 400 500 600 700 800 300 400 500 600 700 800 Orthogonalized Public Expditure on Health Orthogonalized Public Expditure on Health Daat Source: World Bank WDI Daat Source: World Bank WDI (b.1) (b.2) 17 Immunization Measles vs Health Expenditure Immunization Measles vs Health Expenditure 100 OMN KWTAZE ATGHNDLVA DMA SVKHUN DMA SVKHUN CHLLKAEGYVNMUKR IRNKNA 100 OMN BHRSY KA Z W SMROM BLR IRNKNA KA Z BLR R KGZNIC TKMVCT POL LTU MKD CZE KWTAZE ATGUKRLVA R KGZNIC POL LTU CZE TON RUS UZB CHLEGYLKAVNMHNDTKM BHRSY UZBVCT W SMROM MKD ARE MEX JOR JOR PER LCA GRDMDA SLV MNG THAMEX TON RUS URY GRDMDA SLV BRB HRV ARE ALB LCA SAU MNG BRB HRV KOR TT O THAMARALBBRAARMSAU SVN DOMBHSBLZ GMB BGR MARPERBRAARMBGRGMB URY J AM BWAGUY TUNPAN EST ARG SVN KOR TT O DOMBHSBLZ J AM BWA GUY TUNPAN EST ARG MYS LBN LBN CHN DZA ECU CRI MYS DZA CRI ZMB CHNECU ZMB sels 80 GTMPRY FJI GTMPRY FJI MUS VENMWI TJKCOL TUR MUS 80 VENMWI TJKCOL TUR ERISLB PHLSWZVUTGHANZAFZWE KETZA ERISLB KETZA BDI LSO sels PHLSWZVUTGHANZAFZWE BDI LSO IDN GEONPLRWA BGDCPV IDN GEONPLRWA BGDCPV ea ea M BENBOL M BENBOL no CIVMRT AGO NAM CIVMRT YEM NAM LAO COM YEM AGO LAO COM 60 no atiz SEN 60 UGA PNG MOZ SENPNG MOZ GA B INDCMR UGA INDCMR PAKTGOGNB SDNKHM GA B KHM niu GINHTI GNB MDG SLE atiz PAKTGOSLE SDN MDG MLI ETH niu GINHTI MLI m ETH m NGA BFA NGA BFA Im 40 Im CAF NERDJI 40 CAF NERDJI TCD TCD COG ZAR COG ZAR 20 20 300 400 500 600 700 800 300 400 500 600 700 800 Orthogonalized Public Expditure on Health Orthogonalized Public Expditure on Health Daat Source: World Bank WDI Daat Source: World Bank WDI (c.1) (c.2) DALE vs Health Expenditure DALE vs Health Expenditure 70 DMA 70 DMA CHL CZE SVN CHL CZE SVN ATGARM J AM GEO ATGARM VCT J AM POLCRI URY ARGSVK HRV VCT POL CRI URY ARGSVK HRV ycnatcepxE PAN GEO PAN KOR ARE TT O MEX VE N BRB KOR ARE MEX CA VE N BRB LTU HUN TT O BHR L GRDBGR SAU LTU HUN MUS OMNDOM KWTAZE BHRLCA GRDBGR SAU MU S OMN DOM KWTAZE CHN LKA TONTURCOL ESTMKD LKA TONTURCOL ESTMKD MYS ROM BLZDZA CHN KNA EC U HNDMDA PRYUKRLVA ROM UZBRUS SLV BLR TUN MYS UZBRUS SLV BLR TUN 60 THA IRNLBN BLZDZA KNA ECU HNDMDA PRYUKRLVA IDNMARFJIPERBRA ALB GUY JOR W SM BHS PHLEGY 60 THA IDNIRNLBN ALB GUY JOR W SM CPVC KAZPAK SYVNMTJKNIC R ycnatce BHS PHLEGY MARFJIPERBRA R CPV KGZ KAZPAK SYVNMTJKNI KGZ GTM TKMSLB Exp GTM TKMSLB efiL IND BOL MNG BOL MNG VUT de 50 BGDYEM NPL 50 BGDYEM NPL GA B GMB GA B GMB LAO COMPNG efiLde IND VUT stjudAy LAOA COM PNG KHMCOG GHA KHMCOG GHSEN HTI SDN HTI SEN SDN CMR BEN CIV CMR BEN CIV MRT TGO MRT TGO 40 KE NZAF TCD 40 KE NZAF TCD ilitb SWZAGO GIN NGAGNB ERILSO DJI SWZAGO GINGAGNB N TZA ERI LSO DJI ZAR MDG ZAR MDG BFATZA BFA NAM BDI NAM stjudAytilib BDI saiD MOZ ETHMOZ UGA ETH UGA MLIBWAZWE RWA saiD MLIBWAZWE RWA 30 ZMB ZMB NER MWI 30 NER MWI SLE SLE 300 400 500 600 700 800 300 400 500 600 700 800 Orthogonalized Public Expditure on Health Orthogonalized Public Expditure on Health Daat Source: World Bank WDI, Mathers et al (2000) Daat Source: World Bank WDI, Mathers et al (2000) (d.1) (d.1) Figure 8. Health Efficiency Frontier: Single Input and Single Output Several results may be highlighted: a. The input efficiency scores obtained for each of the output indicators are highly correlated. The Spearman rank-order correlation coefficient oscillates between .66 and .94, with a mean of 0.81 (see Tables C.1 and C.2 in Appendix C). This indicates that the efficiency ranking is very similar regardless of the output indicator being used. b. Despite the orthogonalization by GDP the relatively rich countries tend to be in the less efficient group. The group of inefficient producers tend to concentrate in two groups of countries: one group of relatively rich countries like the Czech Republic, Croatia, Slovenia, and Hungary that have big expenditure levels and not extremely high output (input inefficiency) and other group of countries that spend relatively little but their output indicators could be substantially larger, like Sierra Leone, Namibia, Zimbawe, and Lesotho 18 c. To capture this difference, it is convenient to examine the output- efficiency scoring (see Tables C.3 and C.4 in Appendix C). The rankings between input and output orientations are highly correlated. d. With the four output indicators deciles, more efficient and least efficient countries are listed in Table 4. The group of least efficient countries could, on average, increase output significantly for a given expenditure level. For instance, the decile of most inefficient countries could almost double the disability-adjusted life expectancy (DALE) index to achieve the same efficiency as the benchmark. Similarly the DPT immunization would have to triple to achieve the same efficiency level than the benchmark developing countries. e. The regional aggregation of the efficiency scores, by each individual output indicator shows that input efficiency scores (Table 5) are lower than output efficiency scores (Table 6). This is especially true in ECA, LAC and MNA, and to a lesser extent in EAP and SAS. In Africa, both scores are strikingly similar, indicating that, on average, the region spend about 35 percent in excess of the benchmark cases to achieve the same output level. Alternatively, the output level is 35 percent below comparable efficient countries that use the same input (expenditure) level. Table 4. Health Attainment: Single Input, Single Output Input-Efficient Output Efficient More efficient Korea, Malaysia, Thailand, Korea, Dominica, Oman, Trinidad & Tobago, Oman, United Arab Emirates, Anigua United Arab Emirates, and Barbuda Mauritius, Kuwait, Chile Least efficient Argentina, Estonia, Czech Sierra Leone, Ethipia, Republic, Slovenia, Burkina Fasso, Central Macedonia, Croatia, Namibia, African Republic, Mali Tunisia, Latvia, Hungary, Barbados Table 5. Health Attainment: Input-Efficiency scores by regions across the world - Single Input, Single Output AFR EAP ECA LAC MNA SAS Life Expectancy at birth .65 .72 .58 .69 .73 .69 Immunization DPT .66 .73 .63 .68 .76 .71 Immunization Measles .65 .73 .67 .69 .76 .71 DALE .65 .72 .60 .70 .71 .69 19 Table 6. Health Attainment: Output-Efficiency scores by regions across the world - Single Input-Single Output AFR EAP ECA LAC MNA SAS Life Expectancy at birth .63 .87 .91 .92 .90 .83 Immunization DPT .62 .83 .95 .87 .90 .75 Immunization Measles .63 .83 .95 .91 .90 .71 DALE .56 .83 .90 .90 .86 .79 III.3. Multiple Inputs and Multiple Outputs Both education and health attainment are not solely determined by public spending. Other inputs, such as private spending also affect the output indicators. For health, the World Bank WDI database reports a comparable statistic across countries. Unfortunately, a comprehensive database of this variable does not exist for education: For the education production technology we have multiple indicators of educational attainment, and three inputs (public spending, teachers per pupil, and adult literacy rate). In health, besides public spending, two other inputs were included: private spending and the education level of adults. The analysis was limited to include up to three outputs Too many output indicators will complicate the analysis, biasing efficiency scores towards one, increasing the variance of the estimators, and reducing their speed of convergence to the true efficiency estimators (Simar and Wilson, 2000; Groskopff, 1996) In education, the selected input-output combinations produce ranking that are somewhat similar: the average rank correlation coefficient is .53. The frequency distribution of the efficiency estimators is similar in all the models, and as the model shifts from a basic two-input two-output model to a more complex three-input three­output model, the frequency distribution shifts to the right, that is, more concentrated around more efficient results. The multi-input output model results (Table 7) in general confirm the results of Table 1. Some new countries that appear as efficient are Bangladesh, Congo and Argentina. In the case of Bangladesh and Congo, this is the result of considering literacy of adults as a factor of production, that in these countries is low, and hence, appearing as very efficient. Congo has also extremely low ratio of teachers per student, the other factor of production, reinforcing the bias towards the efficient score. Within the least efficient countries, the models point at Zimbabwe, Lesotho, Botswana, Malaysia, and Saudi Arabia as the single- input models. In addition, Costa Rica and Swaziland appear as input inefficient. 20 Table 7. Educational Attainment: Multiple Inputs, Multiple Outputs Input-Efficient Output Efficient More efficient Bangladesh, Bahrain,, Argentina, Bangladesh,, Dominican Republic, Chile, Brazil, Bahrain, Argentina, Estonia Dominican Republic, Congo Least efficient Zimbabwe, Lesotho, Sudan, Ghana, Tanzania, Botswana, Costa Rica, Ethiopia, Kenya, Niger Swaziland, Saudi Arabia, Malaysia The regional aggregation for input and output efficiency scores using the multiple input- output framework show (Tables 8 and 9) that as the model becomes more complex (adding inputs or outputs), scores tend to show more efficient regions. The input efficiency regional aggregation allows several interesting comparisons across the regions on the impact of an additional input on the efficiency scores. For instance, the first two rows of Table 8 allow examination of the impact of adding literacy of adults as an additional input. The biggest impact is in the MNA region, followed by ECA and LAC while the others the increase in efficiency scores is more marginal13. Output efficiency scores change substantially in MNA and Africa. Table 8. Education Attainment: Input-Efficiency scores by regions across the world - Multiple Inputs, Multiple Outputs AFR EAP ECA LAC MNA SAS 2 inputs (public expenditure, teachers per pupil) ­ 2 .88 .83 .72 .82 .73 .91 outputs (gross primary and secondary enroll.) 3 inputs (public expenditure, teachers per pupil, .92 .89 .86 .89 .92 .96 literacy of adult) ­ 2 outputs (gross primary and secondary enroll.) 3 inputs (public expenditure, teachers per pupil, .87 .94 .93 .93 .92 1.0 literacy of adult) ­ 2 outputs (net primary and secondary enroll.) 2 inputs (public expenditure, literacy of adult)- 3 .78 .92 .95 .84 .80 .91 outputs (first complete, second level complete, avg yrs of school) 3 inputs (public expenditure, literacy of adult, .91 .97 .94 .89 .81 .95 teachers per pupil)- 3 outputs (first complete, second level complete, avg yrs of school) 3 inputs (public expenditure, teachers per pupil, .91 .97 .94 .89 .80 .95 literacy of adult) ­ 3 outputs (literacy of youth, first level complete, second level complete) 13The statistical significance of these changes has yet to be determined. The tests developed by Banker , and used in previous sections do not apply to the multiple-output cases we are analyzing here (Simar and Wilson, 2000) 21 Table 9. Education Attainment: Output-Efficiency scores by regions across the world - Multiple Inputs, Multiple Outputs AFR EAP ECA LA MNA SAS 2 inputs (public expenditure, teachers per pupil) ­ 2 .68 .83 .80 .85 .71 .79 outputs (gross primary and secondary enroll.) 3 inputs (public expenditure, teachers per pupil, .82 .88 .89 .89 .91 .90 literacy of adult) ­ 2 outputs (gross primary and secondary enroll.) 3 inputs (public expenditure, teachers per pupil, .79 .97 .96 .96 .92 1.0 literacy of adult) ­ 2 outputs (net primary and secondary enroll.) 2 inputs (public expenditure, literacy of adult)- 3 .64 .87 .94 .80 .79 .83 outputs (first complete, second level complete, avg yrs of school) 3 inputs (public expenditure, literacy of adult, .86 .94 .93 .86 .80 .89 teachers per pupil)- 3 outputs (first complete, second level complete, avg yrs of school) 3 inputs (public expenditure, teachers per pupil, .98 1.0 1.0 .98 .99 .99 literacy of adult) ­ 3 outputs (literacy of youth, first level complete, second level complete) Rows 4 and 5 of Table 8 allow comparing the impact of adding the variable teachers per pupil as an additional input. In Africa the change is dramatic, while in ECA and MNA there is no significant change. Further analysis is required to explain this differential response to the inclusion of this input. In health there are multiple combinations of inputs (public expenditure, private expenditure, and literacy of adults) and outputs (life expectancy at birth, immunization DPT, immunization measles, and Disability Adjusted life expectancy (DALE)). The combinations we selected produce rankings that are more homogeneous. The rank correlation is in the range of .65 to .98 (Tables 10-12). Bangladesh appears as efficient, as well as Niger, mainly due to the inclusion as of the ( low ) levels of literacy of adults as an input, and hence, making these countries to appear as efficient. Table 10. Health Attainment: Multiple Inputs, Multiple Outputs Input-Efficient Output Efficient More efficient Bangladesh, Malaysia, Costa Bangladesh, Costa Rica, Rica, Kuwait, Morocco, Oman, Kuwait, Malaysia, Morocco, Mauritius, Niger Mauritius, Oman, Niger Least efficient Russia, Belarus, Namibia, Namibia, Togo, Ethiopia, Romania, Estonia, Croatia, Mozambique, Cote d"Ivoire, Lituania,, Hungary, Jordan Cameroon, Congo, Central African Republlic, Nigeria, Uganda 22 Table 11. Health Attainment: Input-Efficiency scores by regions across the world - Multiple Inputs, Multiple Outputs AFR EAP ECA LA MNA SAS 2 inputs (public expenditure, literacy of adult) ­ 2 .85 .82 .72 .82 .91 .93 outputs (life expectancy, immunization DPT.) 3 inputs (public expenditure, private spending, .86 .82 .74 .83 .91 .94 literacy of adult) ­ 2 outputs (life expectancy, immunization DPT.) 3 inputs (public expenditure, private spending, .86 .82 .77 .83 .91 .94 literacy of adult) ­ 2 outputs (life expectancy, immunization measles.) 3 inputs (public expenditure, private spending, .86 .82 .80 .87 .93 .94 literacy of adult) ­ 3 outputs (life expectancy, immunization DPT., DALE) Table 12. Health Attainment: Output-Efficiency scores by regions across the world - Multiple Inputs, Multiple Outputs AFR EAP ECA LA MNA SAS 2 inputs (public expenditure, literacy of adult) ­ 2 .81 .91 .97 .93 .97 .96 outputs (life expectancy, immunization DPT.) 3 inputs (public expenditure, private spending, .81 .91 .97 .94 .97 .96 literacy of adult) ­ 2 outputs (life expectancy, immunization DPT.) 3 inputs (public expenditure, private spending, .80 .91 .96 .94 .98 .96 literacy of adult) ­ 2 outputs (life expectancy, immunization measles.) 3 inputs (public expenditure, private spending, .82 .91 .97 .95 .98 .97 literacy of adult) ­ 3 outputs (life expectancy, immunization DPT., DALE) Tables 9 and 12 show that, on average, developing nations score between .85 and .95 in output efficiency in the multiple input-output framework. This figures imply that developing countries could raise their output levels by an average of 10 percent with the same input consumption, if they were as efficient as the comparable benchmark countries. This figure is simply indicative, as the precise estimate varies with the country and with the selected indicator, and has a large variance across countries: for instance, the bottom decile of (output) efficiency scores is about .66, implying that the scope for increasing health and education attainment levels is between 3 or 4 times higher than for the whole sample average. 23 III.4. Efficiency Change Over Time To examine the evolution of input and output efficiency over time, we computed the efficiency scores in two different time periods: 1975-1980 and 1996-2002 for education study, and 1997-99 and 2000-02 for health study, the construction of which is driven by data availability. Appendix D reports the results on a regional basis14. Comparison of different input-output bundles in different time periods has to be done carefully because the frontier can be shifting outward through time. In some cases the frontier displacement can be parallel (such as in the life expectancy case of Figure 9). In others, the frontier displacement can be very uneven (biased frontier shift in Figure 9) reflecting biased technological change (see Appendix D for detailed discussion). Frontier Shift: Life Expectancy Frontier Shift: Gross Secondary Enrollment 78 100 LVA KOR BRB CRI URY ent KWT 80 CRI KWT y mlol ncatc 76 KWT nrE y 60 ARGIDN pexE ondar efLi 74 ecS 40 s GTM KOR osrG 20 OMN KOR 0 72 350 400 450 500 550 600 600 800 1000 1200 Orthogonalized Public Expenditure on Education Orthogonalized Public Expenditure on Education Eff. Frontier 1975-80 Eff. Frontier 1996-02 Eff. Frontier 1997-99 Eff. Frontier 2000-02 Data Source: World Bank WDI Data Source: World Bank WDI Parallel Shift Biased Shift Figure 9. Efficiency Frontier Shift Over Time The detailed comparison between observed input-output combinations in different time periods distinguishes whether variations in the levels of input utilization or output production levels are due to changes in efficiency or changes in technology. This testing is possible with observed levels of inputs and outputs, and are based on the concept of a Malmquist Index (Fare, Grosskpof, Norris and Zhang, 1994). This method has been used to study productivity change in the OECD economies, as well as productivity in agriculture across the world (Coelli and Rao, 2003; Nin, Arndt, and Preckel, 2003). Appendix D describes details of the method that uses some of the efficiency scores calculated in previous sections, and the index that will facilitate the analysis of productivity change through time. 14 Scores for individual countries are available at the PRMED website indicated in footnote 1. 24 Results show that over the two decades output-efficiency growth was faster in the most inefficient countries, showing that there is a "catching-up" phenomenon. However, when measuring input-efficiency, the previous results do not hold: most regions increased expenditure levels without increasing output. Appendix D summarizes, on a regional basis, the change in productivity of public spending decomposed into efficiency change and technological change.15 IV. Explaining Inefficiency Variation Across Countries This chapter seeks to identify factors correlated with inefficiency scores variation across countries. This two-stage approach attempts to identify statistically significant regularities common to efficient or inefficient countries using the more basic statistical techniques. This exercise does not try to identify supply or demand factors that affect health and education outcomes, such as those described by Filmer (2003). The scope is limited to verifying statistical association between the efficiency scores and environmental variables. IV.1. Method, Variables and Data Description Given that the dependent variable, the efficiency scores, is continuous and distributed over a limited interval (between zero and one), it is appropriate to use a censored (Tobit) regression model to analyze the relationships with other variables. The panel consist of a large numebr of countries (varying from 70 to 140 depending on the output indicator) and only two time periods. The literature on panel estimation has shown that in panels with this configuration, that is, a large number of cross-section units (countries) and a relatively short time dimension (2 periods), the fixed-effects estimators of the coefficients will be inconsistent (Maddala, 1987) and their variance will be biased downward (Greene, 2003b). Hence the random effects panel estimation method was preferred. The dependent variable in the Tobit panel is the input efficiency score calculated by DEA method in the first stage. The input-oriented estimator reflects the consideration that input choices are more under the policymaker's control. The independent variables reflect environmental effects included in precursor papers, as well as suggested by others recently. We included the following independent variables16. a. The size of government expenditure. Most of the papers surveyed in the previous section explore the relationship between the size of the government (or expenditure as a percentage of GDP) and efficiency levels. The objective is to verify if additional pubic spending is associated with better education and health outcomes. While some papers have found a negative association between efficiency and expenditure levels (Gupta- Verhoeven 2001, Jarasuriya-Woodon 2003, and Afonso et.al. 2003), others have found a positive association (Evans et.al. 2003) and others have found no significant impact (Filmer and Pritchett, 1999) 15The results on country-by-country basis can be found at the PRMED website indicated in footnote 1. 16The precise definition and sources is can be found in Appendix B, Table B.6. 25 b. A government budget composition variable. Given that both education and health are labor-intensive activities, the government's labor policies will determine the efficiency with which outputs are delivered. We choose a budget composition indicator to reflect this, in particular, the ratio of the wage bill to the total budget. A higher ratio is expected to be negatively correlated with efficiency. c. Per-capita GDP. We included the per-capita GDP to control for the Balassa- Samuleson effect in comparing across countries. If richer countries tend to be more inefficient (given higher wages in these countries), a negative sign is expected. However, it must be recalled that to obtain the efficiency scores in the "fist stage" we constructed an auxiliary variable (the orthogonalized public expenditure). Hence the inclusion of this variable in the second stage is an attempt to control for any remaining Balassa- Samuleson effects. d. Urbanization. The clustering of agents make it cheaper to provide services in urbanized areas rather than in rural. Higher degree of urbanization should reflect in higher efficiency, making positive as the expected sign of the coefficient on this variable. e. Prevalence of AIDS. Based on WHO mappings of the disease, we included a dummy variable in the most severely affected countries to control for the role of this epidemic in the poor health outcomes. Evans et. al. (2000) report that AIDS lowers the Disability adjusted life expectancy (DALE) by 15 years or more. Aids also affects education outcomes both directly and indirectly (Drake, et. al. 2003): directly because school-age children are affected: UNAIDS estimates that almost 4 million children have been infected since the epidemic began, and two thirds have died. However, the indirect channel is relatively more important: AIDS leaves orphaned children that are more likely to drop-out of school or repeat. All these factors reflect how AIDS affect the demand for education. But the supply is also affected by the decreasing teacher labor force due to illness or death, or the need to care for family (Pigozzi, 2004). Prevalence of HIV/AIDS should be negatively associated with education and health outcomes. Consequently, efficiency scores should be negatively associated with the dummy variable. f. Income distribution inequality. Ravallion (2003) argues that, besides the mean income, its distribution affects social indicators because their attainment is mostly determined by the income of the poor. Hence, we controlled for the distribution of income by including the Gini coefficient as an explanatory variable. Higher inequality is expected to be associated with lower educational and health attainments, making negative the expected sign of this variable. g. Share of public sector in the provision of service. Services can be provided by both the public and private sectors, and efficiency indicators will differ across countries depending on the relative productivities of both sectors. Previous studies have included this variable to explain differences in outcomes (Le Grand, 1987; Berger and Messer, 2002) or efficiency scores (Greene, 2003a). The specific variable we included was the ratio of publicly financed service over the total spending (sum of private and public spending). 26 h. External Aid. To the extent that countries do not have to incur the burden of taxation, they may not have the incentive to use resources in the most cost-effective way. Another channel through which aid-financing may affect efficiency is through the volatility and unpredictability of its flows. Given that this financing source is more volatile than other types of fiscal revenue (Bulir and Hamann, 2000), it is difficult to undertake medium- term planning with in activities funded with aid resources. If this is the case, we would expect a negative association between aid-dependence and efficiency in those activities funded with aid, mostly health services. To our knowledge there are no previous attempts to establish a relationship between efficiency and the degree to which activities are financed by external aid. There is, however, recent evidence of a negative association between donor financing and some health outcomes (Bokhari, Gottret, and Gai, 2005) i. Institutional Variables. Countries with better institutions, more transparency, and less corruption are expected to have higher efficiency scores. Similarly, countries that have suffered wars or state failures are expected to register lower efficiency scores. To capture these effects we included different indicators: the ICRG International Country Risk Indicators, the Worldwide Governance Research Indicators, in particular the Control of Corruption component (Kaufmann, et.al, 2002). We also included a dummy variable if there had been some type of state failure, such as internal wars, from the State Failure Task force database. The data on educational and health indicators are not available on a continuous annual basis for many countries. Thus, averages of the variables were computed over sub-periods both in the first stage calculation of efficiency score and in the second stage of regression analysis. Specifically, educational indicators are averaged over two periods (1975-80 and 1996-2002) and health indicators over two periods (1996-99 and 2000-02). This discrepancy in the sub-period construction is due exclusively to the lack of data for earlier years. The averages are treated as separate observations. The advantages of this approach are threefold. First, the averages may serve as a better measure of the educational and health attainment, which can hardly be substantially improved on a yearly basis; Second, the averaging maximizes the coverage of countries for each period, since one observation of a certain year is sufficient to help the country survive in the cross sectional comparison; Third, the time series thus constructed for each country, although short, facilitates the implementation of econometric techniques on panel data to explore the efficiency variations across countries and through time. 27 IV.2. Results The Tobit estimation on panel data is defined as follows. VRSTEit = f (WAGEit,GOVEXPit, PUBTOTit, GDPPCit,URBANit, AIDSit,GINIit, EXTAIDit, INSTit,CONS) where VRSTEit = Variable returns to scale DEA efficiency score for single output and multiple output cases. WAGEit = Wages and salaries (% of total public expenditure) GOVEXPit = Total government expenditure (% of GDP) PUBTOTit = Share of expenditures publicly financed (public/total) GDPPCit = GDP per capita in constant 1995 US dollars URBANit = Urban population (% of total) AIDSit = Dummy variable for HIV/AIDS GINIit = Gini Coefficient EXTAIDit = External aid (% of fiscal revenue) INSTit = Institutional indicators including ICRG country risk, World Governance Research Indicators (Corruption Control), or a dummy for state failures from the State Failure Task Force database. CONS = Constant Tables 13 and 14 report the results for the single-input single-output case and the multiple-input multiple-output case, respectively. The more interesting findings are: a. We find that countries with larger expenditure levels also register the more inefficient scores. This result is robust to changes in the output indicator selected, to considering health or education, and to adopting either the single ­output or multiple output frameworks. The trade-off between size of expenditure and efficiency is quite robust. b. Countries in which the wage bill represents a higher fraction of total expenditure tend to be more inefficient. This result does not hold for health in the multiple output framework. This difference could be due partly to the relatively decreasing number of health care professionals in the world, especially in the poorer countries (Liese, et.al., 2003). Further investigation would be required to examine why this is not the case in education. c. Countries in which public financing is a larger share of total expenditure on the service also register lower efficiency scores. This is probably due to differential productivity rates in the provision of services. Further research would be needed to explain why this is the case in health services. Recent case studies of water 28 companies in Argentina show that private companies were more efficient than public ones and provided better service quality leading to lower child mortality rates (Galiani, Gertler and Schargrodsky, 2005). In education, there is some evidence that efficiency scores are lower in public schools (Alexander and Jaforullah, 2004), though the evidence regarding the impact of privatizing education on outcomes is mixed (World Bank, 2003). d. Urbanization is positively associated with efficiency scores in both education and health. However, when life expectancy is included as an output, the relationship is non-significant (single output) or negative (multiple-output). Possibly the urbanization variable is capturing other effects such as crime. There is ample literature studying the relationship between urbanization and crime (Glaeser E. and B. Sacerdote, 1999). Alternatively, as urbanization intensifies, communicable diseases are more difficult and costly to control, hence the negative association found between both variables in health. e. The effect of the HIV/AIDS is clearly negative affecting health efficiency scores in the multiple-output models. However, its effect on education is less clear, as the expected negative sign is significant in few cases and has the opposite sign in equal number of cases. This confirms the difficulty of empirically verifying this relationship, reported in previous work (Wobst and Arndt, 2003). f. Income distribution has the expected negative effect on the educational and health efficiency scores. The impact of inequality on health scores is less robust than in education, but confirms Greene's findings (2003). Other papers (Berger and Messer, 2002), have found a positive association between income inequality and health outcomes. g. Results showed a negative relationship between some of the efficiency scores and the external aid dependency ratio. Only in one of the multiple-output cases is the external aid associated with higher efficiency, but with border-line statistical significance. Though no causality relationship can be inferred from the exercise, this is one of the results that merit more detailed research. This result might be explained by the volatility of aid as a funding source that limits medium term planning and effective budgeting. Probably this is why the negative sign is more robust in health than in education, given that donor funding is mostly directed towards the first. Recent research (Bokhari, Gottret, Gai, 2005) show a negative association between some health outcomes and the degree of donor funding, pointing in this same direction. This result also coincides with research showing that the quality of policies is not only unrelated to donor financing, but that highly indebted countries with "bad" policies received more net transfers as a share of GDP (Birdsall, et.al. 2003). h. None of the institutional variables proved to be statistically significant. We interpret this result as due to the data limitations, as some of the most crucial information, for instance the corruption index is only available since 1996 and the panel exercise was limited to a cross-section. The state-failure dummy variable or 29 the ICRG indicators did not prove to be significant either. Hence, these results are not reported in any of the tables. To investigate the possibility of slope heterogeneity across countries, we followed the approach used in Haque, Pesaran, and Sharma (1999). Specifically, the slope coefficients in each country are assumed to be fixed over time, but varying across countries linearly with the individual sample mean of GDP per capita. The final results (Tables 15 and 16) only include the statistically significant interaction terms, in order to avoid co linearity arising from the correlation between original explanatory variables and the auxiliary variable capturing the interaction of these with the sample mean of GDP per capita. Hence the estimated model is: VRSTEit = f (WAGEit ,GOVEXPit ,GDPPCit ,URBANit , AIDSit , GINIit ,WAGEGit ,GOVGit ,GINIGitCONS) where VRSTEit = Variable returns to scale DEA efficiency score for single output and multiple output cases WAGEit = Wages and salaries (% of total public expenditure) GOVEXPit = Total government expenditure (% of GDP) PUBTOTit = Share of expenditures publicly financed (public/total) GDPPCit = GDP per capita in constant 1995 US dollars URBANit = Urban population (% of total) AIDSit = Dummy variable for HIV/AIDS GINIit = Gini Coefficient CONS = Constant WAGEGit = WAGEit *GDPPCi GOVGit = GOVEXPit *GDPPCi GINIGit = GINIit *GDPPCi GDPPCi = T -1 T t=1GDPPCit Results show that the interaction terms are significant, especially for the health regression, implying that there is a heterogeneous response of efficiency scores to the different explanatory variables. This confirms Greene's (2003) results on the WHO data. One of the key results of this section is that the negative association between the size of government expenditure and efficiency is stronger in countries with higher per-capita GDP. Similarly, this happens with the wage variable. Results are somewhat similar to those of the homogeneous slopes, though statistical significance of many of the coefficients is lower. This is the result of co-linearity between the auxiliary variables and the original set of explanatory variables. This problem deserves further work in the future. 30 Interpretation of these results requires caution due to several limitations. First, education and health outcomes are explained by multiple supply and demand factors (Filmer, 2003) that are not included here. This is not the object of the present paper. The omission of one of these factors in the health or education production functions in the previous stage could explain some of the cross-country co-variation of the efficiency results (Ravallion, 2003). The goodness-of-fit analysis of the first stage indicated that no important factor seemed to be omitted. Of course, there can always be additional factors that could be included but the curse of dimensionality17 is particularly pressing in non-parametric statistical methods (even if the data were available) The second limitation derives from the intuitive question why the set of explanatory variables used in the second stage were not included in the first stage. The answer lies in that most of these variables are environmental and outside the control of the decision- making unit. The inclusion of these environmental variables would have had little justification from the production function perspective. Additionally, by maintaining the production function as simple as possible the dimensionality curse is avoided. Finally, the third limitation arises from the fact that if the variables used in the first stage to obtain the efficiency estimator are correlated with the second stage explanatory variables, the coefficients will be inconsistent and biased (Simar and Wilson, 2004; Grosskopf, 1996; Ravallion, 2003). To examine the extent of this potential problem we calculated correlation coefficients between the "first-stage" inputs and the second stage explanatory variables. The largest correlation coefficients were between GDP per capita and the teachers per pupil ratio and the literacy of the adult. To examine the sensitivity of the results to the inclusion of GDP per capita, all the estimations were performed without this variable and none of the results changed. V. Concluding Remarks and Directions for Future Work The paper presented an application of non-parametric methods to analyze the efficiency of public spending. Based on a sample of more than 140 countries, the paper estimated efficiency scores for nine education output indicators and fourth health output indicators. Our results indicate that countries could achieve substantially higher education and health output levels: on average, developing countries score output efficiency of about .9 (in the multiple input-output framework) or around .7 (in the single input-single output model), implying that they could increase health and education attainment between by 10 percent or 30 percent while consuming the same input level, if they were as efficient as the comparable benchmark countries. This is just an indicative figure, as the figures vary across countries and with the selected output indicator. It is crucial to identify what are the institutional or economic factors that cause some countries to be more efficient than others in the service delivery. 17As the number of outputs increase, the number of observations must increase exponentially to maintain a given mean-square error of the estimator. See Simar and Wilson (2000). 31 In terms of policy implications, it is vital to differentiate between the technically efficient level and the optimal or desired spending level. Even if a country is identified as an "efficient" benchmark country, it may very well still need to expand its public spending levels to achieve a target level of educational or health attainment indicators. Such is the case of countries with low spending levels and low attainment indicators, close to the origin of the efficient frontier.. The important thing is that countries expand their scale of operation along the efficient frontier. The methods used in the paper can be interpreted as tools to identify extreme cases of efficient units and inefficient cases. Once the cases have been identified, more in-depth analysis is required to explain departures from the benchmark, as proposed and done by Sen (1981). Given that the methods are based on estimating the frontier directly from observed input-output combinations they are subject to sampling variability and are sensitive to the presence of outliers. Recent advances allow dealing with these problems such as in Wilson (2004). Additionally, it would be useful to contrast these results with those obtained with the use of parametric stochastic frontier estimation. In a "second stage" the paper verified statistical association between the efficiency scores and environmental variables that are not under the control of the decision-making units. The panel Tobit regressions showed that the variables, which are negatively associated with efficiency scores, include the size of public expenditure, the share of the wage bill in the total public budget, the proportion of the service that is publicly financed, the prevalence of HIV/AIDS epidemic on health efficiency scores, income inequality on education efficiency scores, and external aid-financing on some of the efficiency scores. This last impact is probably due to the volatility of aid that impedes effective medium term planning and budgeting, and probably explains why the result is more robust in health than in education where most of the donor-funding is directed. This result point in the same direction of previous research showing that donor financing is unrelated to the quality of domestic policies and that, in the case of highly indebted counties, those with worse policies received more transfers. A positive association between urbanization and efficiency outcomes is also identified in education but some of the health efficiency scores are negatively associated. This last result probably is due to higher crime rates in the cities or the effect of communicable diseases that spread with agglomeration. These are topics for further research in case studies. 32 Table 13. Explaining cross-country variation in efficiency, Single Input-Single Output Independent Gross Net Gross Net Literacy of Average First Secondary Life Immuni- Immuni- Variable Primary Primary Secondary Secondary Youth Years of Level Level Expectancy zation zation Enrollment Enrollment Enrollment Enrollment School Complete Complete DPT Measles WAGE -.00117*** -.00357* -.00172** -.00680* -.00189** -.00570* -.00470** -.00546* .00065 -.00052 -.00049 GOVEXP -.00387* -.00546* -.00340* -.00455** -.00387* -.00696* -.00566* -.00765* -.00269** -.00078 -.00227*** PUBTOT -- -- -- -- -- -- -- -- -.00213* -.00150* -.00135*** GDPPC -.00002* -.00002* -.00001* .00002** -.00002* -1.5e-6 -.00001 -7.7e-6 7.6e-7 -.00001* -.00001* URBAN .00167* .00143*** .00168* .00037 .00187* .00532* .00551* .00555* -.00018 .00099** .00088 AIDS -.04471** -.08731** -.02204 .01243 -.02974 .12717*** .1211*** .11041 -.05473 -.01108 -.02730 GINI -.06688 .01507 -.19326** -.42311 -.18484*** -.44658** -.34402 -.45870** .22118 .09510 .08692 EXTAID -.00094 -.00196** -.00021 -.00106 -.00054 .00089 -.00025 -.00006 -.00224*** -.00155 -.00324** CONS 1.02996* 1.1282* 1.0472* .84138* 1.0697* .76791* .70009* .81705* .79193* .78734* .84384* # of Obs 79 44 79 34 72 71 71 71 118 118 118 (# of Countrs) (51) (30) (51) (20) (46) (45) (45) (45) (69) (69) (69) Wald Chi2(6) 83.91 66.09 46.72 55.31 44.27 64.13 45.53 61.94 50.83 123.97 35.01 (Prob > Chi2) (.00) (.00) (.00) (.00) (.00) (.00) (.00) (.00) (.00) (.00) (.00) Note: * 0.01 significance level, ** 0.05 significance level, *** 0.10 significance level, and insignificant otherwise 33 Table 14. Explaining cross-country variation in efficiency, Multiple Inputs-Multiple Outputs Independent EDU2-2 EDU2-2n EDU3-2 EDU3-2n EDU3-3 EDU3-3bl HEA2-2 HEA3-2 HEA3-2m HEA3-3 Variable WAGE -.00212** -.00767* -.00219** -.00425 -.001000 -.00340*** .00126* .00205* .00203*** .00203*** GOVEXP -.00321* -.00365 -.00203*** .00099 -.00123*** -.00316*** -.0012*** -.00273* -.0009 -.00090 PUBTOT -- -- -- -- -- -- -.00151* -.00142* -.00159*** -.00151*** GDPPC -.00001** -6.6e-7 -.00001*** -.00003 -4.2e-6 1.98e-6 -2.7e-6 4.2e-6* -7.1e-7 -9.3e-7 URBAN .00138*** -.00045 .00191** .001997 .00127* .00091 -.00095* -.00148* -.00106 -.00105 AIDS -.03295 -.05843 -.00956 -.14763 .01797 .06022 -.04815* -.033147** -.07162 -.06999 GINI -.06485 .43602 -.14717 .27058 -.17237** -.15697 -.03997 -.07958*** -.01015 -.01387 EXTAID .00010 -.00622 .00152 -.00274 -.00066 .00123 .00087 .00128*** -.00095 -.00106 CONS 1.0655* 1.0223 1.0642* 1.0124* 1.06570* 1.1218* 1.0098 1.0117* .98891* .98787* # of Obs 76 34 69 32 69 63 97 98 98 98 (# of Countrs) (49) (20) (44) (19) (44) (40) (55) (56) (56) (56) Wald Chi2(6) 24.48 11.69 20.84 7.44 18.72 9.18 185.21 229.98 19.25 18.62 (Prob > Chi2) (.00) (.11) (.00) (.38) (.01) (.24) (.00) (.00) (.01) (.02) Note: * 0.01 significance level, ** 0.05 significance level, *** 0.10 significance level, and insignificant otherwise EDU2-2: Inputs: orthogonalized public spending on education per capita, teachers per pupil Outputs: gross primary and secondary enrollments EDU2-2n: same inputs as EDU2-2, outputs: net primary and secondary enrollment EDU3-2: literacy of adult is added to EDU2-2 as input EDU3-2n: literacy of adult is added to EDU2-2n as input EDU3-3: literacy of youth is added to EDU3-2 as output EDU3-3bl: same inputs as in EDU3-2, outputs: average years of school, first level complete, and second level complete (Barro-Lee education indicators) HEA2-2: Inputs: orthogonalized public spending on health per capita, literacy of adult Outputs: life expectancy at birth, and immunization DPT HEA3-2: orthogonalized private spending on health per capita is added to HEA2-2 as input HEA3-2m: Immunization Measles is in place of DPT in HEA3-2 as output HEA3-3: Immunization Measles is added to HEA3-2 as output 34 Table 15. Explaining cross-country variation in efficiency, Single Input and Single output - Heterogeneous Slopes Independent Gross Net Gross Net Literacy of Average First Secondary Life Immuni- Immuni- Variable Primary Primary Secondary Secondary Youth Years of Level Level Expectancy zation zation Enrollment Enrollment Enrollment Enrollment School Complete Complete DPT Measles WAGE -.00006 .00076 -.00035 -.00228 -.00056 -.00200 -.00120 -.00419 -.00306*** -.00079 -.00241 GOVEXP -.00363* -.00255*** -.00377* -.00727*** -.00552* -.00595*** -.00453 -.00611*** .00337** .00168*** .00221 PUBTOT -- -- -- -- -- -- -- -- -.00162* -.00162* -.00097 GDPPC -.00002* -.00002* -5.4e-6 .00003* -.00002*** .00004* .00003*** .00003*** .00002** -.00002* -.00001 URBAN .00179* .00132** .00193* .00139 .00212* .00566* .00601* .00593* -.00080 -.00117* .00021 AIDS -.03866*** -.06603** -.03153 .01010 -.02177 .05491 .06656 .06464 -.02321 -.04147** -.00826 GINI -.14230 -.42098* -.14976 -.29395 -.13107 -.09995 -.15463 -.24762 -.12865 -.38851* -.42162** WAGG -4.4e-6*** -1.2e-6* -4.6e-7*** -9.4e-7 -4.5e-7 -8.1e-7 -8.8e-7 -2.4e-7 8.9e-7** 6.95e-8 5.1e-7 GOVG -8.6e-8 -5.2e-7*** 4.3e-8 3.6e-7 4.0e-7 -4.3e-7 -4.4e-7 -5.3e-7 -1.4e-6* -5.4e-7* -9.4e-7* GINIG .00003 .00011* -2.4e-6 -.00003 2.0e-6 -.00006 -.00005 -.00006 .00001 .00009* .00006*** CONS 1.0156* 1.1036* 1.0098* .74603* 1.0365* .60371* .53977* .68648* .82665* 1.0119* .93820* # of Obs 82 47 82 36 75 74 74 74 120 121 121 (# of Countrs) (52) (31) (52) (21) (47) (46) (46) (46) (70) (71) (71) Wald Chi2(6) 87.32 93.98 62.74 105.34 58.40 94.00 69.32 82.38 74.33 450.54 52.71 (Prob > Chi2) (.00) (.00) (.00) (.00) (.00) (.00) (.00) (.00) (.00) (.00) (.00) Note: * 0.01 significance level, ** 0.05 significance level, *** 0.10 significance level, and insignificant otherwise 35 Table 16. Explaining cross-country variation in efficiency, Multiple Inputs and Multiple Outputs - Heterogeneous Slopes Independent EDU2-2 EDU2-2n EDU3-2 EDU3-2n EDU3-3 EDU3-3bl HEA2-2 HEA3-2 HEA3-2m HEA3-3 Variable WAGE .00051 -.00140 .00005 .00494 -.00018 -.00045 -.00063 -.00065 -.00093 -.00092 GOVEXP -.00323** .00501 -.00385** .00520 -.00256** -.00459 .00122*** .00063 -.00070 -.00064 PUBTOT -- -- -- -- -- -- -.00180* -.00145** -.00149*** -.00141*** GDPPC -8.6e-6 .00002 1.7e-6 .00003 -1.8e-6 -2.1e-6 -.00001** -.00001 -.00003** -.00003** URBAN .00137** .00079 .00166** .00096 .00134* .00064 -.00246* -.00167*** -.00160 -.00159 AIDS -.04139 -.06211 -.04744 -.20362* .00646 .04633 -.06289* -.04001 -.07217 -.07025 GINI -.14418 -.18676 .07096 -.02601 -.07474 -.20029 -.32844* -.45695** -.29885 -.30857 WAGG -8.3e-7** -1.2e-6 -6.4e-7*** -1.9e-6 -2.0e-7 -7.9e-7 7.8e-7* 7.2e-7 6.0e-7 6.0e-7 GOVG -6.3e-8 -2.6e-6*** 3.5e-7 -1.2e-6 3.0e-7 3.5e-7 -5.98e-7* -4.9e-7 2.7e-8 1.4e-8 GINIG .00003 .00012 -.00003 .00005 -.00002 .00003 .00005* .00005*** .00006 .00006*** CONS 1.0515* .89986* 1.0021* .84756* 1.0464 1.1257* 1.1494* 1.1457* 1.1512* 1.1495* # of Obs 79 36 72 34 72 66 101 101 101 101 (# of Countrs) (50) (21) (45) (20) (45) (41) (58) (58) (58) (58) Wald Chi2(6) 41.93 18.57 31.15 18.71 23.89 13.22 600.70 37.22 25.33 24.74 (Prob > Chi2) (.00) (.03) (.00) (.22) (.00) (.15) (.00) (.00) (.00) (.01) Note: 1. * 0.01 significance level, ** 0.05 significance level, *** 0.10 significance level, and insignificant otherwise 2. 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Data Envelopment Analysis (DEA) Model A measure of production efficiency, perhaps the simplest one, is defined as the ratio of output to input. It is, however, inadequate to deal with the existence of multiple inputs and outputs. The relative efficiency for all decision-making units (DMU), j=1,...,n, is then modified as the ratio of weighted outputs to weighted inputs, more precisely, s ur yrj Relative efficiency = r=1 (A.1) m i=1vixij where x and y are inputs and outputs, respectively, and u and v are the common weights assigned to outputs and inputs, respectively. A challenge of this measure immediately follows: it is difficult to justify the common weights given that DMUs may value inputs and outputs differently. The seminal paper by Charnes, Cooper and Rhodes (1978) proposed the following ratio form to allow for difference in weights across DMUs, which establishes the foundation of data envelopment analysis (DEA). s Max h0 = r=1 r yr0 m i=1ixi0 subject to : s r=1 r yrj (A.2) m 1, j =1,L,n i=1ixij r , r =1,L,s i , i =1,L,m > 0 In the model, there are j=1,..., n observed DMUs which employ i =1,..., m inputs to produce r =1,..., s outputs. One DMU is singled out each time, designated as DMU0, to be evaluated against the observed performance of all DMUs. The objective of model (A.2) is to find the most favorable weights, r and i , for DMU0 to maximize the relative efficiency. The constraints are that the same weights will make ratio for every DMU be less than or equal to unity. The optimal value of the ratio must be 0 h0 1 and DMU0 * is efficient if and only h0 =1, otherwise it is considered as relatively inefficient. One * problem with the ratio formulation is that there are an infinite number of solutions: if r andi are solutions to (A.2), so are r andi, > 0. It is worth observing one important feature of model (A.2). In maximizing the objective function it is the relative magnitude of the numerator and the denominator that really matters and not their individual values. It is thus equivalent to setting the denominator to a constant, say 1, and maximizing the numerator. This transformation will not only lead 40 to the uniqueness of solution but also convert the fractional formulation of model (A.2) into a linear programming problem in model (A.3). s Max ryr0 r=1 subject to : m ixi0 = 1 i=1 (A.3) s m ryrj - ixij 0, j =1,L,n r=1 i=1 -r -, r = 1,L,s -i -, i = 1,L,m Model (A.3) facilitates straightforward interpretation in terms economics. The objective is now to maximize the weighted output per unit weighted input under various conditions, the most critical one of which is that the virtual output does not exceed the virtual input for any DMU. Since model (A.3) is a linear programming, we can convert the maximization problem into a minimization problem, e.g. a dual problem, by assigning a dual variable to each constraint in the primal (A.3). Specifically, dual variables , j , sr , si are assigned as + - follows. s Max Dual Variable ryr0 r=1 subject to : m ixi0 = 1 i=1 (A.3') s m ryrj - ixij 0, j =1,L,n j r=1 i=1 - r -, r =1,L,s sr + -i -, i =1,L,m si- A dual minimization problem is thus derived as model (A.4). It is clear that model (A.4) has m+s constraints while model (A.3) has n+m+s+1 constraints. Since n is usually considerably larger than m+s, the dual DEA significantly reduces the computational burden and is easier to solve than the primal. 41 Min -i=1 si + sr m s - + r=1 subject to : n xi0 - xijj - si = 0 - j=1 (A.4) n yr0 = y rjj - sr + j=1 j 0, sr 0, si 0 + - i = 1,L,m, r = 1,L,s, j =1,L,n More importantly, the duality theorem of linear programming states that the solution value to the objective function in (A.4) is exactly equal to that in (A.3). And, the dual variables, (1,2,L,n), have the interpretation of Lagrange multipliers. That is, the value of a dual variable is equal to the shadow price of Lagrange Multiplier. It is also known that, from constrained optimization problem, j > 0 normally when the constraint in (A.3') is binding and j = 0 if not. Note that the binding constraint in (A.3) implies that the corresponding DMU is efficient. In another word, efficient units are identified by positive 's while inefficient units are given 's of zero. The DMU in question in model (A.4) is thus compared with the efficient DMUs only, named as comparison peers in the literature. The solution values of 's reflect the exact weights assigned to each peer in the evaluation of DMU0. Since only efficient DMUs exert effective constraints in model (A.4), as argued above, the input-output bundle, ( n n j=1xij j , j=yrjj ), is the most efficient combination for i = 1,L,m and r =1,L,s . To achieve an output level yr0 , which is as close as possible to n j= yrjj , DMU0 has to use an input bundle to meet the minimum requirement, n j=1xij j . This further implies that the solution * is the lowest proportion of the current input bundle, xi0 used by DMU0 , that is actually required to meet the minimum input requirement and produce target output yr0 . The solution * is defined as the efficiency score for DMU0. For instance, * = 0.60 implies that 40 percent of current input is a waste of resources. Model (A.4) also offers the explanation why the data envelopment analysis is so named. The first constraint in (A.4) defines a lower limit of inputs and the second constraint an upper limit of outputs for DMU0, and within the limits is minimized. The set of solutions to all DMUs forms an upper bound that envelops all observations. 42 Appendix B. Table B.1 Efficiency Score for Selected Education Indicators Primary School Enrollment Secondary School Enrollment Input Efficiency Output Efficiency Input Efficiency Output Efficiency Country FDH DEA FDH DEA FDH DEA FDH DEA AGO 0.702 0.702 0.502 0.490 0.702 0.702 0.157 0.132 ARG 0.813 0.761 0.838 0.838 0.726 0.651 0.922 0.711 ARM 0.707 0.707 0.703 0.690 0.707 0.707 0.883 0.746 AZE 0.709 0.690 0.729 0.695 0.682 0.682 0.793 0.650 BDI 0.665 0.665 0.410 0.410 0.665 0.665 0.087 0.070 BEN 0.678 0.678 0.668 0.635 0.678 0.678 0.217 0.177 BFA 0.700 0.700 0.324 0.315 0.700 0.700 0.098 0.082 BGD 0.727 0.702 0.722 0.702 0.699 0.699 0.404 0.338 BGR 0.883 0.807 0.857 0.809 0.769 0.769 0.932 0.809 BHR 0.999 0.907 0.915 0.901 0.999 0.941 0.998 0.954 BHS 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 BLR 0.692 0.663 0.766 0.766 0.603 0.603 0.667 0.667 BLZ 0.747 0.707 0.846 0.846 0.581 0.581 0.496 0.496 BOL 0.732 0.712 0.794 0.794 0.626 0.626 0.549 0.549 BRA 1.000 1.000 1.000 1.000 0.779 0.709 0.932 0.761 BRB 0.460 0.433 0.752 0.752 0.636 0.472 0.786 0.786 BWA 0.494 0.463 0.747 0.747 0.430 0.430 0.551 0.551 CAF 0.697 0.697 0.500 0.485 0.697 0.697 0.097 0.081 CHL 0.842 0.776 0.866 0.782 0.733 0.733 0.813 0.707 CHN 1.000 0.949 1.000 0.953 0.778 0.778 0.693 0.607 CIV 0.656 0.656 0.538 0.538 0.656 0.656 0.234 0.186 CMR 0.699 0.699 0.708 0.689 0.699 0.699 0.284 0.238 COG 0.715 0.715 0.607 0.601 0.715 0.715 0.423 0.361 COL 0.768 0.754 0.801 0.801 0.657 0.657 0.692 0.550 COM 0.668 0.668 0.585 0.585 0.668 0.668 0.251 0.202 CPV 0.910 0.902 0.942 0.942 0.659 0.659 0.620 0.495 CRI 0.703 0.670 0.761 0.761 0.612 0.612 0.426 0.426 CZE 0.719 0.670 0.743 0.743 0.626 0.626 0.680 0.680 DJI 0.680 0.680 0.292 0.278 0.680 0.680 0.170 0.139 DMA 0.561 0.556 0.710 0.710 0.620 0.550 0.702 0.702 DOM 1.000 1.000 1.000 1.000 0.856 0.856 0.609 0.574 DZA 0.723 0.698 0.772 0.772 0.629 0.629 0.519 0.519 ERI 0.671 0.671 0.404 0.404 0.671 0.671 0.251 0.203 EST 0.478 0.476 0.717 0.717 0.731 0.586 0.835 0.835 ETH 0.661 0.661 0.383 0.383 0.661 0.661 0.156 0.125 FJI 0.741 0.690 0.835 0.835 0.577 0.577 0.596 0.596 GAB 1.000 1.000 1.000 1.000 0.724 0.724 0.487 0.419 GEO 0.711 0.711 0.708 0.697 0.711 0.711 0.763 0.647 GHA 0.666 0.666 0.564 0.564 0.666 0.666 0.363 0.292 GIN 0.726 0.726 0.507 0.469 0.726 0.726 0.136 0.118 GMB 0.677 0.677 0.566 0.566 0.677 0.677 0.320 0.261 GNB 0.686 0.686 0.516 0.495 0.686 0.686 0.145 0.120 43 Table B.1 (continued) Primary School Enrollment Secondary School Enrollment Input Efficiency Output Efficiency Input Efficiency Output Efficiency Country FDH DEA FDH DEA FDH DEA FDH DEA GRD 0.651 0.651 0.678 0.678 0.651 0.651 0.633 0.500 GTM 0.857 0.829 0.840 0.812 0.824 0.824 0.324 0.297 GUY 0.758 0.740 0.796 0.796 0.649 0.649 0.826 0.650 HND 0.762 0.731 0.767 0.767 0.663 0.663 0.323 0.259 HRV 0.657 0.657 0.669 0.669 0.657 0.657 0.878 0.699 HUN 0.696 0.642 0.735 0.735 0.826 0.681 0.757 0.757 IDN 0.913 0.900 0.966 0.904 0.795 0.795 0.593 0.528 IND 0.709 0.702 0.747 0.713 0.682 0.682 0.478 0.392 IRN 0.625 0.625 0.677 0.677 0.625 0.625 0.634 0.634 JAM 0.599 0.591 0.708 0.708 0.576 0.576 0.622 0.622 JOR 0.583 0.583 0.679 0.679 0.583 0.583 0.613 0.613 KAZ 0.708 0.687 0.726 0.692 0.681 0.681 0.894 0.733 KEN 0.631 0.631 0.643 0.643 0.631 0.631 0.296 0.228 KGZ 0.775 0.713 0.733 0.733 0.675 0.675 0.843 0.686 KHM 0.827 0.809 0.824 0.821 0.720 0.720 0.212 0.182 KNA 0.809 0.759 0.840 0.840 1.000 1.000 1.000 1.000 KOR 0.762 0.741 0.815 0.736 1.000 0.839 1.000 0.870 KWT 0.406 0.406 0.645 0.645 0.406 0.406 0.666 0.666 LAO 0.897 0.817 0.861 0.837 0.698 0.698 0.347 0.291 LBN 0.880 0.840 0.900 0.846 0.766 0.766 0.840 0.726 LCA 0.573 0.565 0.805 0.805 0.490 0.490 0.642 0.642 LKA 0.852 0.835 0.926 0.845 0.742 0.742 0.808 0.681 LSO 0.602 0.594 0.807 0.807 0.515 0.515 0.248 0.248 LTU 0.710 0.647 0.725 0.725 0.710 0.654 0.722 0.722 LVA 0.548 0.541 0.707 0.707 0.527 0.527 0.684 0.684 MAC 1.000 1.000 1.000 1.000 0.962 0.962 0.889 0.863 MAR 0.628 0.628 0.679 0.679 0.628 0.628 0.304 0.304 MDA 0.613 0.613 0.626 0.626 0.613 0.613 0.572 0.572 MDG 0.708 0.697 0.742 0.707 0.680 0.680 0.152 0.124 MEX 0.752 0.740 0.802 0.802 0.644 0.644 0.700 0.548 MKD 0.766 0.694 0.722 0.722 0.667 0.667 0.798 0.643 MLI 0.679 0.679 0.382 0.363 0.679 0.679 0.128 0.104 MNG 0.655 0.634 0.688 0.688 0.630 0.630 0.647 0.497 MOZ 0.682 0.682 0.629 0.601 0.682 0.682 0.108 0.088 MRT 0.677 0.677 0.603 0.603 0.677 0.677 0.197 0.161 MUS 0.792 0.759 0.806 0.776 0.690 0.690 0.738 0.611 MWI 0.911 0.901 0.941 0.941 0.660 0.660 0.175 0.140 MYS 0.530 0.523 0.707 0.707 0.509 0.509 0.526 0.526 NAM 0.572 0.531 0.832 0.832 0.446 0.446 0.469 0.469 NER 0.680 0.680 0.249 0.237 0.680 0.680 0.067 0.055 NIC 0.773 0.712 0.734 0.734 0.673 0.673 0.526 0.427 NPL 0.871 0.807 0.830 0.830 0.678 0.678 0.401 0.328 OMN 0.742 0.742 0.692 0.632 0.742 0.742 0.763 0.643 44 Table B.1 (continued) Primary School Enrollment Secondary School Enrollment Input Efficiency Output Efficiency Input Efficiency Output Efficiency Country FDH DEA FDH DEA FDH DEA FDH DEA PAK 0.712 0.712 0.528 0.522 0.712 0.712 0.261 0.222 PAN 0.701 0.678 0.774 0.774 0.610 0.610 0.527 0.527 PER 1.000 0.919 1.000 0.926 0.727 0.727 0.775 0.670 PHL 0.890 0.810 0.860 0.831 0.692 0.692 0.789 0.655 PNG 0.732 0.732 0.654 0.590 0.732 0.732 0.205 0.178 POL 0.554 0.549 0.710 0.710 0.727 0.608 0.766 0.766 PRY 0.747 0.732 0.800 0.800 0.639 0.639 0.555 0.432 ROM 0.821 0.758 0.774 0.767 0.715 0.715 0.806 0.687 RUS 0.852 0.837 0.945 0.849 0.729 0.729 0.875 0.758 RWA 0.800 0.792 0.851 0.815 0.685 0.685 0.130 0.107 SAU 0.414 0.414 0.504 0.504 0.414 0.414 0.519 0.519 SDN 0.616 0.616 0.398 0.398 0.616 0.616 0.220 0.220 SEN 0.663 0.663 0.513 0.513 0.663 0.663 0.171 0.137 SLB 0.708 0.690 0.731 0.696 0.680 0.680 0.181 0.148 SLE 0.684 0.684 0.492 0.470 0.684 0.684 0.167 0.137 SLV 0.902 0.858 0.930 0.861 0.785 0.785 0.518 0.457 SVK 0.752 0.692 0.733 0.733 0.655 0.655 0.881 0.699 SWZ 0.666 0.642 0.771 0.771 0.580 0.580 0.387 0.387 SYR 0.792 0.748 0.794 0.764 0.690 0.690 0.428 0.354 TCD 0.686 0.686 0.510 0.489 0.686 0.686 0.107 0.088 TGO 0.901 0.834 0.885 0.885 0.653 0.653 0.328 0.259 THA 0.605 0.605 0.667 0.667 0.605 0.605 0.513 0.513 TJK 0.784 0.724 0.775 0.740 0.683 0.683 0.790 0.649 TON 0.675 0.662 0.801 0.801 0.788 0.659 0.766 0.766 TTO 0.810 0.743 0.769 0.753 0.705 0.705 0.785 0.662 TUN 0.643 0.590 0.824 0.824 0.500 0.500 0.565 0.565 TUR 0.746 0.725 0.728 0.723 0.717 0.717 0.677 0.579 TZA 0.676 0.676 0.467 0.467 0.676 0.676 0.059 0.048 UGA 0.949 0.869 0.921 0.886 0.690 0.690 0.129 0.107 UKR 0.659 0.659 0.585 0.585 0.899 0.724 0.968 0.772 URY 1.000 0.986 1.000 0.985 1.000 0.945 1.000 0.957 UZB 0.612 0.612 0.655 0.655 0.835 0.678 0.748 0.748 VCT 0.581 0.532 0.728 0.728 0.506 0.506 0.548 0.548 VNM 0.813 0.794 0.823 0.808 0.708 0.708 0.638 0.540 VUT 0.603 0.578 0.766 0.766 0.525 0.525 0.203 0.203 WSM 0.675 0.671 0.716 0.716 0.649 0.649 0.729 0.574 YEM 0.627 0.627 0.544 0.544 0.627 0.627 0.324 0.324 ZAF 0.621 0.577 0.833 0.833 0.555 0.484 0.693 0.693 ZMB 0.682 0.682 0.610 0.582 0.682 0.682 0.259 0.212 ZWE 0.549 0.510 0.741 0.741 0.478 0.478 0.344 0.344 45 Table B.2. Efficiency Score for Selected Education Indicator - Learning scores ­ Excluding Developed Countries Learning Input Efficiency Output Efficiency Learning Input Efficiency Output Efficiency Country Score FDH DEA FDH DEA Country Score FDH DEA FDH DEA HUN 542 1.000 1.000 1.000 1.000 HND 396 0.294 0.294 0.731 0.731 SVK 535 1.000 1.000 1.000 1.000 PER 392 0.525 0.525 0.742 0.733 CZE 530 0.972 0.800 0.991 0.990 VUT 375 0.152 0.152 0.692 0.692 RUS 528 1.000 1.000 1.000 1.000 KEN 349 0.232 0.232 0.644 0.644 BGR 515 1.000 1.000 1.000 1.000 PHL 345 0.382 0.382 0.645 0.639 MYS 506 0.169 0.169 0.934 0.934 MUS 342 0.606 0.606 0.648 0.644 LVA 504 0.178 0.177 0.930 0.930 BLZ 335 0.216 0.216 0.618 0.618 POL 504 0.198 0.198 0.930 0.930 MAR 334 0.255 0.255 0.616 0.616 LTU 485 0.321 0.319 0.895 0.895 ZWE 331 0.122 0.122 0.611 0.611 THA 475 0.265 0.262 0.876 0.876 TZA 329 0.282 0.282 0.607 0.607 ROM 472 0.552 0.547 0.894 0.884 CMR 322 0.345 0.345 0.594 0.594 MDA 464 0.220 0.218 0.856 0.856 MOZ 318 0.297 0.297 0.587 0.587 MEX 455 0.382 0.377 0.850 0.842 SWZ 317 0.206 0.206 0.585 0.585 TTO 454 0.652 0.644 0.860 0.857 MDG 315 0.293 0.293 0.581 0.581 MKD 453 0.386 0.381 0.847 0.838 UGA 309 0.315 0.315 0.570 0.570 JOR 439 0.211 0.208 0.810 0.810 BWA 288 0.107 0.107 0.531 0.531 TUN 437 0.150 0.148 0.806 0.806 BFA 277 0.329 0.329 0.511 0.511 IRN 435 0.289 0.284 0.803 0.803 CIV 269 0.269 0.269 0.496 0.496 ARG 432 0.456 0.449 0.807 0.804 ZAF 261 0.149 0.149 0.482 0.482 TUR 431 0.565 0.556 0.816 0.809 MLI 233 0.291 0.291 0.430 0.430 BRA 428 0.456 0.448 0.800 0.797 NAM 232 0.113 0.113 0.428 0.428 IDN 419 0.826 0.811 0.814 0.804 LSO 230 0.142 0.142 0.424 0.424 CHL 407 1.000 1.000 1.000 1.000 ZMB 228 0.295 0.295 0.421 0.421 PRY 406 0.288 0.288 0.749 0.749 SEN 223 0.277 0.277 0.411 0.411 BOL 405 0.239 0.239 0.747 0.747 MWI 207 0.261 0.261 0.382 0.382 COL 400 0.354 0.354 0.748 0.739 NER 173 0.292 0.292 0.319 0.319 KWT 398 0.114 0.114 0.734 0.734 Note: Data for learning scores are reproduced from Table 1.2. in Crouch and Fasih (2004). Sorted by learning scores. 46 Table B.3. Efficiency Score for Selected Education Indicator - Learning scores ­ Including Developed Countries Learning Input efficiency Output efficiency Learning Input efficiency Output efficiency Country Scores FDH DEA FDH DEA Country Scores FDH DEA FDH DEA NLD 543 1.000 1.000 1.000 1.000 IRN 435 0.747 0.747 0.801 0.801 HUN 542 0.918 0.916 0.998 0.998 ARG 432 0.814 0.814 0.796 0.796 SVK 535 0.956 0.936 0.985 0.985 TUR 431 0.806 0.806 0.794 0.794 AUS 533 0.987 0.961 0.982 0.982 BRA 428 0.795 0.795 0.788 0.788 AUT 533 0.755 0.735 0.982 0.982 IDN 419 0.815 0.815 0.772 0.772 CAN 532 0.818 0.794 0.980 0.980 CHL 407 0.850 0.850 0.750 0.750 CHE 531 0.807 0.781 0.978 0.978 PRY 406 0.745 0.745 0.748 0.748 CZE 530 0.967 0.933 0.976 0.976 BOL 405 0.716 0.716 0.746 0.746 SWE 529 0.555 0.534 0.974 0.974 COL 400 0.771 0.771 0.737 0.737 FIN 528 0.682 0.654 0.972 0.972 KWT 398 0.636 0.636 0.733 0.733 RUS 528 0.957 0.918 0.972 0.972 DOM 397 0.877 0.877 0.768 0.741 GBR 517 1.000 0.972 1.000 0.981 HND 396 0.740 0.740 0.729 0.729 BGR 515 0.931 0.899 0.948 0.948 PER 392 0.797 0.797 0.722 0.722 FRA 515 0.724 0.699 0.948 0.948 VUT 375 0.655 0.655 0.691 0.691 DEU 514 0.991 0.955 0.994 0.969 KEN 349 0.708 0.708 0.643 0.643 USA 509 0.888 0.842 0.937 0.937 PHL 345 0.769 0.769 0.635 0.635 MYS 506 0.760 0.715 0.932 0.932 MUS 342 0.826 0.826 0.630 0.630 ESP 505 0.977 0.917 0.977 0.943 BLZ 335 0.712 0.712 0.617 0.617 LVA 504 0.765 0.715 0.928 0.928 MAR 334 0.727 0.727 0.615 0.615 POL 504 0.790 0.739 0.928 0.928 ZWE 331 0.617 0.617 0.610 0.610 NZL 501 0.648 0.601 0.923 0.923 TZA 329 0.728 0.728 0.606 0.606 NOR 500 0.486 0.449 0.921 0.921 CMR 322 0.753 0.753 0.593 0.593 ISL 499 0.674 0.620 0.919 0.919 MOZ 318 0.735 0.735 0.586 0.586 DNK 493 0.451 0.407 0.908 0.908 SWZ 317 0.703 0.703 0.584 0.584 GRC 491 1.000 1.000 1.000 1.000 MDG 315 0.733 0.733 0.580 0.580 ITA 486 0.876 0.876 0.940 0.906 UGA 309 0.742 0.742 0.569 0.569 LTU 485 0.768 0.768 0.893 0.893 BWA 288 0.603 0.603 0.530 0.530 THA 475 0.739 0.739 0.875 0.875 BFA 277 0.746 0.746 0.510 0.510 PRT 474 0.663 0.663 0.873 0.873 CIV 269 0.727 0.727 0.495 0.495 ROM 472 0.804 0.804 0.869 0.869 ZAF 261 0.668 0.668 0.481 0.481 CYP 468 0.674 0.674 0.862 0.862 MLI 233 0.732 0.732 0.429 0.429 ISR 467 0.498 0.498 0.860 0.860 NAM 232 0.610 0.610 0.427 0.427 MDA 464 0.700 0.700 0.855 0.855 LSO 230 0.641 0.641 0.424 0.424 MEX 455 0.785 0.785 0.838 0.838 ZMB 228 0.734 0.734 0.420 0.420 TTO 454 0.825 0.825 0.836 0.836 SEN 223 0.730 0.730 0.411 0.411 MKD 453 0.777 0.777 0.834 0.834 MWI 207 0.720 0.720 0.381 0.381 JOR 439 0.702 0.702 0.808 0.808 NER 173 0.733 0.733 0.319 0.319 TUN 437 0.657 0.657 0.805 0.805 Note: Data for learning scores are reproduced from Table 1.2. in Crouch and Fasih (2004). Sorted by learning scores. 47 Table B.4 Efficiency Score for Selected Health Indicators Life Expectancy at Birth Immunization DPT Input Efficiency Output Efficiency Input Efficiency Output Efficiency Country FDH DEA FDH DEA FDH DEA FDH DEA AGO 0.671 0.671 0.609 0.607 0.671 0.671 0.368 0.368 ALB 0.697 0.697 0.955 0.953 0.826 0.792 0.984 0.984 ARE 1.000 1.000 1.000 1.000 0.956 0.942 0.983 0.967 ARG 0.527 0.492 0.955 0.955 0.478 0.478 0.811 0.811 ARM 0.712 0.663 0.963 0.959 0.681 0.651 0.906 0.906 ATG 0.744 0.736 0.980 0.978 0.800 0.794 0.997 0.997 AZE 0.724 0.724 0.862 0.861 0.857 0.822 0.984 0.984 BDI 0.638 0.638 0.549 0.547 0.638 0.638 0.746 0.746 BEN 0.649 0.649 0.693 0.690 0.649 0.649 0.737 0.737 BFA 0.647 0.647 0.580 0.577 0.647 0.647 0.405 0.405 BGD 0.672 0.672 0.798 0.795 0.672 0.672 0.821 0.821 BGR 0.619 0.619 0.931 0.926 0.652 0.650 0.954 0.954 BHR 0.736 0.736 0.955 0.954 0.872 0.834 0.983 0.983 BHS 0.755 0.755 0.907 0.906 0.795 0.770 0.921 0.921 BLR 0.560 0.560 0.892 0.886 0.664 0.659 0.997 0.997 BLZ 0.797 0.749 0.966 0.964 0.723 0.723 0.893 0.893 BOL 0.633 0.633 0.816 0.812 0.633 0.633 0.714 0.714 BRA 0.672 0.672 0.888 0.886 0.672 0.672 0.892 0.892 BRB 0.721 0.632 0.987 0.979 0.556 0.556 0.899 0.899 BWA 0.626 0.626 0.535 0.533 0.741 0.695 0.975 0.975 CAF 0.649 0.649 0.571 0.569 0.649 0.649 0.436 0.436 CHL 0.964 0.879 0.990 0.990 0.881 0.787 0.958 0.958 CHN 0.717 0.717 0.917 0.916 0.717 0.717 0.890 0.890 CIV 0.679 0.679 0.600 0.598 0.679 0.679 0.605 0.605 CMR 0.694 0.694 0.661 0.659 0.694 0.694 0.482 0.482 COG 0.648 0.648 0.670 0.667 0.648 0.648 0.317 0.317 COL 0.623 0.623 0.931 0.927 0.623 0.623 0.773 0.773 COM 0.664 0.664 0.792 0.790 0.664 0.664 0.701 0.701 CPV 0.643 0.643 0.898 0.895 0.643 0.643 0.805 0.805 CRI 1.000 1.000 1.000 1.000 0.528 0.528 0.899 0.899 CZE 0.386 0.372 0.964 0.964 0.414 0.402 0.988 0.988 DJI 0.612 0.612 0.610 0.607 0.612 0.612 0.404 0.404 DMA 0.749 0.728 0.997 0.990 0.684 0.682 0.999 0.999 DOM 0.776 0.776 0.895 0.881 0.776 0.776 0.688 0.688 DZA 0.696 0.696 0.920 0.918 0.734 0.700 0.905 0.905 ECU 0.694 0.694 0.909 0.907 0.694 0.694 0.861 0.861 EGY 0.715 0.715 0.884 0.883 0.753 0.747 0.948 0.948 ERI 0.626 0.626 0.666 0.662 0.626 0.626 0.825 0.825 EST 0.515 0.515 0.910 0.910 0.543 0.541 0.952 0.952 ETH 0.644 0.644 0.556 0.554 0.644 0.644 0.482 0.482 FJI 0.702 0.702 0.902 0.900 0.740 0.706 0.905 0.905 GAB 0.804 0.804 0.700 0.691 0.804 0.804 0.452 0.452 GEO 0.689 0.689 0.954 0.951 0.689 0.689 0.824 0.824 48 Table B.4 (continued) Life Expectancy at Birth Immunization DPT Input Efficiency Output Efficiency Input Efficiency Output Efficiency Country FDH DEA FDH DEA FDH DEA FDH DEA GHA 0.657 0.657 0.749 0.746 0.657 0.657 0.765 0.765 GIN 0.671 0.671 0.605 0.604 0.671 0.671 0.470 0.470 GMB 0.636 0.636 0.696 0.693 0.670 0.655 0.932 0.932 GNB 0.632 0.632 0.585 0.583 0.632 0.632 0.495 0.495 GRD 0.647 0.647 0.946 0.943 0.681 0.671 0.939 0.939 GTM 0.714 0.714 0.848 0.847 0.714 0.714 0.788 0.788 GUY 0.600 0.600 0.823 0.818 0.600 0.600 0.877 0.877 HND 0.645 0.645 0.862 0.859 0.764 0.683 0.958 0.958 HRV 0.380 0.380 0.945 0.945 0.400 0.394 0.939 0.939 HTI 0.647 0.647 0.690 0.688 0.647 0.647 0.431 0.431 HUN 0.450 0.450 0.921 0.921 0.533 0.533 1.000 1.000 IDN 0.770 0.770 0.862 0.861 0.770 0.770 0.749 0.749 IND 0.718 0.718 0.821 0.820 0.718 0.718 0.633 0.633 IRN 0.740 0.740 0.898 0.897 0.877 0.857 0.991 0.991 JAM 0.835 0.711 0.984 0.980 0.644 0.644 0.886 0.886 JOR 0.585 0.585 0.934 0.928 0.693 0.634 0.967 0.967 KAZ 0.725 0.725 0.838 0.836 0.858 0.807 0.977 0.977 KEN 0.648 0.648 0.621 0.618 0.648 0.648 0.820 0.820 KGZ 0.654 0.654 0.869 0.866 0.774 0.754 0.990 0.990 KHM 0.678 0.678 0.704 0.702 0.678 0.678 0.518 0.518 KNA 0.708 0.708 0.924 0.923 0.838 0.832 0.997 0.997 KOR 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 KWT 1.000 1.000 1.000 1.000 0.914 0.863 0.978 0.978 LAO 0.666 0.666 0.700 0.698 0.666 0.666 0.544 0.544 LBN 0.712 0.712 0.919 0.918 0.750 0.737 0.937 0.937 LCA 0.694 0.694 0.940 0.938 0.694 0.694 0.874 0.874 LKA 0.715 0.715 0.952 0.951 0.847 0.800 0.978 0.978 LSO 0.600 0.600 0.548 0.545 0.600 0.600 0.843 0.843 LTU 0.546 0.546 0.938 0.930 0.575 0.566 0.939 0.939 LVA 0.617 0.617 0.915 0.911 0.731 0.655 0.960 0.960 MAR 0.739 0.739 0.883 0.882 0.779 0.775 0.951 0.951 MDA 0.621 0.621 0.875 0.871 0.736 0.662 0.961 0.961 MDG 0.646 0.646 0.713 0.710 0.646 0.646 0.540 0.540 MEX 0.758 0.758 0.955 0.954 0.898 0.812 0.962 0.962 MKD 0.501 0.501 0.941 0.941 0.527 0.525 0.952 0.952 MLI 0.644 0.644 0.554 0.552 0.644 0.644 0.496 0.496 MNG 0.615 0.615 0.850 0.846 0.647 0.643 0.949 0.949 MOZ 0.625 0.625 0.562 0.559 0.625 0.625 0.606 0.606 MRT 0.651 0.651 0.663 0.660 0.651 0.651 0.439 0.439 MUS 0.936 0.936 0.973 0.955 0.936 0.936 0.937 0.932 MWI 0.627 0.627 0.510 0.508 0.627 0.627 0.853 0.853 MYS 0.949 0.949 0.989 0.975 1.000 1.000 1.000 1.000 NAM 0.543 0.543 0.628 0.623 0.543 0.543 0.723 0.723 49 Table B.4 (continued) Life Expectancy at Birth Immunization DPT Input Efficiency Output Efficiency Input Efficiency Output Efficiency Country FDH DEA FDH DEA FDH DEA FDH DEA NER 0.646 0.646 0.591 0.589 0.646 0.646 0.264 0.264 NGA 0.659 0.659 0.620 0.617 0.659 0.659 0.290 0.290 NIC 0.628 0.628 0.895 0.891 0.661 0.634 0.909 0.909 NPL 0.658 0.658 0.767 0.764 0.658 0.658 0.733 0.733 OMN 0.931 0.858 0.976 0.970 1.000 1.000 1.000 1.000 PAK 0.693 0.693 0.821 0.819 0.693 0.693 0.582 0.582 PAN 0.579 0.559 0.965 0.965 0.553 0.553 0.955 0.955 PER 0.700 0.700 0.905 0.903 0.737 0.710 0.915 0.915 PHL 0.748 0.748 0.904 0.904 0.748 0.748 0.769 0.769 PNG 0.628 0.628 0.748 0.744 0.628 0.628 0.541 0.541 POL 0.550 0.550 0.954 0.946 0.651 0.634 0.990 0.990 PRY 0.676 0.676 0.918 0.916 0.676 0.676 0.723 0.723 ROM 0.558 0.558 0.908 0.902 0.661 0.644 0.990 0.990 RUS 0.617 0.617 0.864 0.860 0.650 0.635 0.931 0.931 RWA 0.636 0.636 0.523 0.521 0.636 0.636 0.847 0.847 SAU 0.615 0.615 0.946 0.941 0.648 0.645 0.951 0.951 SDN 0.685 0.685 0.749 0.747 0.685 0.685 0.473 0.473 SEN 0.640 0.640 0.684 0.681 0.640 0.640 0.582 0.582 SLB 0.607 0.607 0.894 0.890 0.607 0.607 0.801 0.801 SLE 0.635 0.635 0.488 0.486 0.635 0.635 0.449 0.449 SLV 0.634 0.634 0.912 0.908 0.668 0.664 0.949 0.949 SVK 0.464 0.464 0.944 0.944 0.549 0.549 1.000 1.000 SVN 0.380 0.375 0.971 0.971 0.363 0.357 0.939 0.939 SWZ 0.710 0.710 0.631 0.630 0.710 0.710 0.804 0.804 SYR 0.699 0.699 0.910 0.908 0.736 0.735 0.955 0.955 TCD 0.642 0.642 0.633 0.631 0.642 0.642 0.264 0.264 TGO 0.660 0.660 0.644 0.641 0.660 0.660 0.564 0.564 THA 0.786 0.786 0.913 0.900 0.931 0.859 0.970 0.970 TJK 0.650 0.650 0.884 0.881 0.650 0.650 0.827 0.827 TKM 0.639 0.639 0.851 0.848 0.757 0.726 0.984 0.984 TON 0.655 0.655 0.927 0.924 0.776 0.696 0.960 0.960 TTO 0.883 0.883 0.964 0.962 0.930 0.903 0.965 0.939 TUN 0.547 0.547 0.942 0.934 0.648 0.598 0.970 0.970 TUR 0.627 0.627 0.908 0.904 0.627 0.627 0.811 0.811 TZA 0.634 0.634 0.589 0.587 0.634 0.634 0.821 0.821 UGA 0.647 0.647 0.556 0.554 0.647 0.647 0.586 0.586 UKR 0.650 0.650 0.887 0.884 0.770 0.767 0.999 0.999 URY 0.570 0.540 0.959 0.959 0.544 0.531 0.929 0.929 UZB 0.639 0.639 0.889 0.885 0.757 0.726 0.984 0.984 VCT 0.613 0.613 0.953 0.948 0.725 0.715 0.994 0.994 VEN 0.724 0.661 0.958 0.954 0.657 0.657 0.633 0.633 VNM 0.681 0.681 0.901 0.899 0.717 0.701 0.931 0.931 VUT 0.683 0.683 0.889 0.887 0.683 0.683 0.807 0.807 50 Table B.4 (continued) Life Expectancy at Birth Immunization DPT Input Efficiency Output Efficiency Input Efficiency Output Efficiency Country FDH DEA FDH DEA FDH DEA FDH DEA WSM 0.582 0.582 0.902 0.896 0.689 0.646 0.975 0.975 YEM 0.646 0.646 0.736 0.733 0.646 0.646 0.662 0.662 ZAF 0.620 0.620 0.645 0.642 0.620 0.620 0.784 0.784 ZAR 0.648 0.648 0.599 0.597 0.648 0.648 0.280 0.280 ZMB 0.629 0.629 0.511 0.509 0.629 0.629 0.811 0.811 ZWE 0.595 0.595 0.535 0.532 0.595 0.595 0.791 0.791 51 Table B.5. List of Countries Code Region Country Code Region Country Code Region Country AGO AFR Angola GMB AFR Gambia, The OMN MNA Oman ALB ECA Albania GNB AFR Guinea-Bissau PAK SAS Pakistan ARE MNA United Arab Emirates GRD LAC Grenada PAN LAC Panama ARG LAC Argentina GTM LAC Guatemala PER LAC Peru ARM ECA Armenia GUY LAC Guyana PHL EAP Philippines ATG LAC Antigua and Barbuda HND LAC Honduras PNG EAP Papua New Guinea AZE ECA Azerbaijan HRV ECA Croatia POL ECA Poland BDI AFR Burundi HTI LAC Haiti PRY LAC Paraguay BEN AFR Benin HUN ECA Hungary ROM ECA Romania BFA AFR Burkina Faso IDN EAP Indonesia RUS ECA Russian Federation BGD SAS Bangladesh IND SAS India RWA AFR Rwanda BGR ECA Bulgaria IRN MNA Iran, Islamic Rep. SAU MNA Saudi Arabia BHR MNA Bahrain JAM LAC Jamaica SDN AFR Sudan BHS LAC Bahamas, The JOR MNA Jordan SEN AFR Senegal BLR ECA Belarus KAZ ECA Kazakhstan SLB EAP Solomon Islands BLZ LAC Belize KEN AFR Kenya SLE AFR Sierra Leone BOL LAC Bolivia KGZ ECA Kyrgyz Republic SLV LAC El Salvador BRA LAC Brazil KHM EAP Cambodia SVK ECA Slovak Republic BRB LAC Barbados KNA LAC St. Kitts and Nevis SVN ECA Slovenia BWA AFR Botswana KOR EAP Korea, Rep. SWZ AFR Swaziland CAF AFR Central African Rep. KWT MNA Kuwait SYR MNA Syrian Arab Republic CHL LAC Chile LAO EAP Lao PDR TCD AFR Chad CHN EAP China LBN MNA Lebanon TGO AFR Togo CIV AFR Cote d'Ivoire LCA LAC St. Lucia THA EAP Thailand CMR AFR Cameroon LKA SAS Sri Lanka TJK ECA Tajikistan COG AFR Congo, Rep. LSO AFR Lesotho TKM ECA Turkmenistan COL LAC Colombia LTU ECA Lithuania TON EAP Tonga COM AFR Comoros LVA ECA Latvia TTO LAC Trinidad and Tobago CPV AFR Cape Verde MAR MNA Morocco TUN MNA Tunisia CRI LAC Costa Rica MDA ECA Moldova TUR ECA Turkey CZE ECA Czech Republic MDG AFR Madagascar TZA AFR Tanzania DJI MNA Djibouti MEX LAC Mexico UGA AFR Uganda DMA LAC Dominica MKD ECA Macedonia, FYR UKR ECA Ukraine DOM LAC Dominican Republic MLI AFR Mali URY LAC Uruguay DZA MNA Algeria MNG EAP Mongolia UZB ECA Uzbekistan ECU LAC Ecuador MOZ AFR Mozambique VCT LAC St. Vincent & Grenadines EGY MNA Egypt, Arab Rep. MRT AFR Mauritania VEN LAC Venezuela, RB ERI AFR Eritrea MUS AFR Mauritius VNM EAP Vietnam EST ECA Estonia MWI AFR Malawi VUT EAP Vanuatu ETH AFR Ethiopia MYS EAP Malaysia WSM EAP Samoa FJI EAP Fiji NAM AFR Namibia YEM MNA Yemen, Rep. GAB AFR Gabon NER AFR Niger ZAF AFR South Africa GEO ECA Georgia NGA AFR Nigeria ZAR AFR Congo, Dem. Rep. GHA AFR Ghana NIC LAC Nicaragua ZMB AFR Zambia GIN AFR Guinea NPL SAS Nepal ZWE AFR Zimbabwe 52 Table B.5. Continued Developed countries included in the efficiency estimation for learning scores Code Country Code Country Code Country AUS Australia ESP Spain LUX Luxembourg AUT Austria FIN Finland NLD Netherlands CAN Canada FRA France NOR Norway CHE Switzerland GBR United Kingdom NZL New Zealand CYP Cyprus GRC Greece SWE Sweden DEU Germany ISL Iceland USA United States DNK Denmark ITA Italy 53 Table B.6. Definition and Source of Variables Definition of Variable Source Output variables for education School enrollment, primary (% gross) World Bank WDI School enrollment, primary (% net) World Bank WDI School enrollment, secondary (% gross) World Bank WDI School enrollment, secondary (% net) World Bank WDI Literacy rate, youth total (% of people ages 15-24) World Bank WDI Average years of school, ages 15+ Barro-Lee Database First level complete, ages 15+ Barro-Lee Database second level complete, ages 15+ Barro-Lee Database Learning scores Crouch and Fasih (2004) Input variables for education Public education spending per capita in PPP terms, calculated World Bank WDI Literacy rate, adult total (% of people ages 15 and above) World Bank WDI Teachers per pupil, equal the reciprocal of pupils per teacher World Bank WDI Output variables for health Life expectancy at birth, total (years) World Bank WDI Immunization, DPT (% of children ages 12-23 months) World Bank WDI Immunization, measles (% of children ages 12-23 months) World Bank WDI Disability Adjusted Life Expectancy Mathers et al (2000) Input variables for health Literacy rate, adult total (% of people ages 15 and above) World Bank WDI public spending on health per capita in PPP terms, calculated World Bank WDI public spending on health per capita in PPP terms, calculated World Bank WDI Variables used in the calculation World Bank WDI Pupil-teacher ratio, primary World Bank WDI Public spending on education, total (% of GDP) World Bank WDI GDP per capita, PPP (constant 1995 international $) World Bank WDI Health expenditure, private (% of GDP) World Bank WDI Health expenditure, public (% of GDP) World Bank WDI Variables used in the Panel Tobit regression Wages and salaries (% of total public expenditure) World Bank WDI Total government expenditure (% of GDP) World Bank WDI Share of expenditures publicly financed (public/total) World Bank WDI GDP per capita in constant 1995 US dollars World Bank WDI Urban population (% of total) World Bank WDI Dummy variable for HIV/AIDS WHO mappings of diseases Gini Coefficient World Bank WDI Aid (% of fiscal revenue) calculated as Official development assistance World Bank WDI and official aid (current US$) *official exchange rate * PPP conversion factor / Revenue, excluding grants (current LCU) a. The State Failure Task Institutional Indicators including Force a. State Failure data b. ICRG Online Website b. ICRG International Country Risk Indicators c. Kaufmann, et al. 1999a,b c. Worldwide Governance Research Indicators and 2002 54 Figure B. 1. Efficiency Frontiers for Education Free Disposable Hull (FDH) Data Envelopment Analysis (DEA) Net Primary Enrollment vs Education Expenditure Net Primary Enrollment vs Education Expenditure 100 CPVARG ME X FJI BR B CPVARG ME X FJI BR B CHN PAN POL MYS 100 PAN TUN EST CHN POL MYS KORROMGEORWA PERMUS SYR WSMBOL TJK TUN EST VNM MKD BRA GUYL KNATU BLZ TON BHR KORROMGEORWA PERMUS VNM MKD SYR WSMBOL TJK BRA GUYL KNATU BLZ TON DZA BLR JAM BHR DZA BLR JAM URY IDNBGR TURPHL TTO PRYCR IDNBGR TURPHL I TTO ZAF JOR LVA VU TVCT ZAF URY PRYCR I JOR LVA VU TVCT DOM LBNCHL KHMUGAHND BGD DOM BGD DMA LBNCHL KHMUGAHND SVKCZEHUN HRV TGOMNG DMA ent MAC SLV ARMKAZCOLDIR SVKCZEHUN HRV TGOMNG MAC SLV ARM IND NTHA ent KAZCOLDIR IND NTHA ml KGZGR NAM KGZGR ZWE NAM 80 GTM AZE ZWE GABLAOAZE BWA MAR NIC MARMDA SWZ ol KWT PNG GABLAO NIC MDA SWZ BWA ml 80 GTM KWT ol PNG nrE OMN UKR OMN UKR LSO LSO NPL GMB nrE NPL GMB PAKZMB MDG BEN KEN PAKZMB MDG BEN KEN MRT hoolcSy MRT YE M 60 YE M GHA SEN 60 GHA SEN SAU CIV SAU hoolcS CIV TCD TCD MOZ y MOZ COM COM ar GIN TZA ar GIN TZA mirP GNB SDN GNB SDN BDI BDI 40 mirP 40 MLIETH MLIETH etN ERI AGO BFA etN ERI AGO BFA DJI DJI NE R NE R 20 20 300 400 500 600 700 800 300 400 500 600 700 800 Orthogonalized Public Expditure on Education Orthogonalized Public Expditure on Education Data Source: World Bank WDI Data Source: World Bank WDI (a.1) (a.2) Gross Secondary Enrollment vs Education Expenditure Gross Secondary Enrollment vs Education Expenditure 0 0 15 15 ent KNA nte KNA mlolrnE mllo EST BR B 0 EST 100 KOR nrE BRB UKR UZB HUN TON POL KOR UZB HUN TON POL oolhcS URYBHR BRA 10 UKR ARGLTU ol URYBHR BHS LTU BGR DMA BRA ARG RUSARMKAZHRV SVK CZE ZAF DMA BLR LVA KWT BHS BGR LVA ZAF LCA RUS ARMKAZHRV SVK CZE BLR KWT MAC LBNCHROMTJK LKAGEOAZE PER PHLMKD LTTOKGZGUY IRN JOR JAM KGZGUYIRN LCA FJI MAC LBNCHLTTO JOR JAM yr OMN MUS WSM BWA OMNGEOAZE LKAROMTJK PERPHLMKD FJI MUS WSMBOL MDA BWA CPV MNGTHABLZ MYS VCT TUN MYS VCT TUN MEX BOL MDA hocSy CHN TUR COL DZAPAN SAU COL MEX VN M TUR DZAPAN SAU CPV GR D MN GTHABLZ CHN VNM GRD ndaoceS DOM NAM ID N NAM PRY CRI dar DOM IDN 50 PRY CRI SLV NIC GAB IND SWZ on 50 SLV NIC GAB SWZ COGSYR ZWE IND BGDNPL YEM MAR COGSYR ZWE BGD YEM s NPL MAR GTM LAOGMBTGOKEN GHA ecS HND LSO s LAOGMBTGOKEN GHA HND LSO osr SDN GTM PNG KHM BENCI PAKZMB CMRERICOMV VUT G MRT GINAGOMLI GNBETH SLEMWI SLB DJISEN MDG osr SDN PNG KHM BENCIV PAKZMB CMRERICOM VUT GNBETH SLEMWI SLB DJISEN MRT UGA TCD RWA BFA CAF MOZ G UGA TCD RWA MDG NER GINAGOMLI TZA BDI BFA CAFMOZ 0 NER TZA BDI 0 300 400 500 600 700 800 Orthogonalized Public Expditure on Education 300 400 500 600 700 800 Orthogonalized Public Expditure on Education Data Source: World Bank WDI Data Source: World Bank WDI (b.1) (b.2) Net Secondary Enrollment vs Education Expenditure Net Secondary Enrollment vs Education Expenditure 0 0 10 10 KOR KOR UKR KNA LTU EST UKR KNA EST CZE POL LT U CZE POL HU N BRB BRB ent HU N BHR BGR KAZ L VA ent BHR BGR KAZ L VA mllornE 80 HR V HR V BH S ARM AR GBLRJOR 80 BH S ARM AR GBLRJOR ROMAZEMKD TJK SVK JAM FJI JAM FJI DMA KWT ROMAZEMKD TJK SVK DMA KW T URY T OBRAGUYIRN T ON MAC CHLTTOBRAGUYIRN GEO TON URY GEO MD A MYSLCA CHLT MD A MYSLCA LBN MAC LBN OMN WSMBOL TUN mllornE W SMBOL T UN MUS OMN ol MUS 60 MNGPAN ZAF ol MNGPAN ZAF PER VNM DZA BLZ PER VNM DZA BLZ MEX 60 hocS COL COLMEX TURPHL T UR PHL CPV BW A SAU CPV BW A SAU ID N hocS ID N yradnoceSteN GRD CRI GRD CRI SLV PRY PRY BGD SLV 40 BGD DOM SYR ZWE 40 DOM SYR ZW E NI C NAM NAM YEM NI C YEM GHA MAR SWZ VUT VUT GTM GT M PNGL AOGMBTGOKEN PNG L AOGMBTGOKEN 20 KHM BEN ERI LSO 20 KHM BENERI LSO DJI MRT DJI MRT MD G ETH yradnoceSteN GHA MAR SW Z GIN MD G ET H MOZ GIN BFA BDI TCD BFACD TMOZ BDI NER TZA NER T ZA 0 0 300 400 500 600 700 800 300 400 500 600 700 800 Orthogonalized Public Expditure on Education Orthogonalized Public Expditure on Education Daat Source: World Bank WDI Data Source: W orld Bank W DI (c.1) (c.2) 55 Average Years of School vs Education Expenditure Average Years of School vs Education Expenditure KOR KOR 10 POL BGR ROM ROM SVK CZE )+ 10 POL BGR SVK CZE HUN HUN ARG ARG PAN BRB 15 PAN BR 8 PHL FJI 8 PHL FJI hoolcS URY CHL TTO PER PER ME X ME X LKA age(l URY CHL T TO JOR MYS LKA JOR MYS ofsr CHN T HA HR V THA CHN 6 GUY KWT BWA HR V GUY KWT BWA MUS PRY CRI SWZ ZAF 6 MUS PRY CRI SWZ ZAF SYR hoocS SYR ZMB BOL TUR DZA BOL eaY DZA SLV TUR COL IRN JAM ZWE DOM SLV COL ZMB IRN JAM ZWE IDN BRACOG INDHND TUN of DOM IDN BRACOG IND TUN NIC s NIHND C KEN LSO 4 KEN LSO age 4 PAK GHA PAK GHA GTM CMRUGA ervA TGO MWI earY GT M CMR UGA TMWI GO PNG PNG RWA TZA BGDSLSEN CAFNP RWA TZA GA B BGDSL L CAFNPSEN BEN E age BENL E 2 SDN GA B MOZ NER ervA 2 SDN MOZ GNB NER GNB MLI MLI 0 0 0 100 200 300 400 0 100 200 300 400 Orthogonalized Public Expditure on Education Orthogonalized Public Expditure on Education Daat Source: World Bank WDI, Barro-Lee database Data Source: World Bank WDI (d.1) (d.2) Second Level Complete vs Education Expenditure Second Level Complete vs Education Expenditure KOR KOR 40 40 )+ )+ 15 15 ega( 30 MUS gea( 30 MUS teelp ROM ROM PHL teelp moClev PHL 20 CZE PAN 20 CZE PAN SVK POL KWT SVK POL KWT ME X ME X CHN LKA FJI CHN LKA FJI Le HRV MYS HRV MYS BGR PAKHUNZMB PAKHUN PRY IRN moCleveL BGR ZMB IRN CHL CHL PRY ndoceS TTO PER TTO PER 10 ARG JOR TUN BRB 10 ARG JOR TUN BRB URY IDN COL GUY HNDDZA JAM BWA URY IDN COL GUY HND DZA JAM BWA COG SYR COG SYR TURBRA INDNP L CRI THA BOL dnoceS INDNP L CRI THABOL DOM BGD TURBRA ZAF DOM BGD ZAF GTMSLV CMRNIC CAFBEN GHA LSO CMRNIC CAFBEN GHA LSO GA BPNG UGASEN SDNSWZ 0 RWA MWI SDNSWZ GTMSLV GA B PNG GNB MOZ SL ETGO NER MLI ZWE UGASEN TZA KEN 0 RWA MWI GNB MOZ SLETGO NER MLI ZWE TZA KEN 0 100 200 300 400 0 100 200 300 400 Orthogonalized Public Expditure on Education Orthogonalized Public Expditure on Education Daat Source: World Bank WDI, Barro-Lee database Data Source: World Bank WDI, Barro-Lee database (e.1) (e.2) Literacy of Youth vs Education Expenditure Literacy of Youth vs Education Expenditure 0 10 MAC URY RUS TJKUKR HUNBLR LVA EST BRB BHR BHR URY BGRCHLTTO ARM SVK PRYCRI UZB PEVNMBRA RPHL WSMLTU TONFJI IDN CHNOMNLKATUR BGRCHLTTO RUS ROMKAZSVKARGCRI ARM TJKUKR HRV LVA EST BRB RPHL WSMLTU MNGHUNBLRJOR MDA UZB TONFJI MAC ROM KAZHRVARGMDAMNGTHA JOR COG THA 100 COLMEXBOL PRY PAN MYS ZWE IDN CHNOMNLKATUR COG COLMEXBOL PAN MYS ZWE BLZ MUS KEN BLZ PEVNMBRA KEN IRN JAM MUS IRN JAM DOM SAUKWT SAUKWT CMRGHA NAM TZA SWZ LSO TUNZAF NAM DOM CMRGHA TZA SWZ LSOTUNZAF SLV SYRCPV DZA ZMB BWA SLV SYRCPV DZA ZMB BWA HND HND RWA RWA 80 GTM 80 KHMUGA GTM LAO KHMUGA LAO SDN htuoY SDN NICTGO h NICTGO INDMWI outY INDMWI MAR TCD MAR TCD YEM of CAF BDI YEM of CAF BDI MOZCIV NPL ycarte 60 MOZCIV NPL 60 COM y COM PA K PA K ETH ac ETH BEN BEN SEN ert MRT SEN BGDMRT BGD Li Li 40 40 MLI MLI NER NER 20 20 BFA BFA 300 400 500 600 700 800 300 400 500 600 700 800 Orthogonalized Public Expditure on Education Orthogonalized Public Expditure on Education Data Source: World Bank WDI Daat Source: World Bank WDI (f.1) (f.2) 56 Appendix C. Table C.1. Spearman rank-correlation on input efficiency rankings (FDH) Gross Net Gross Seconda Net Seconda Avg. First Second Life Immunizat Primary ry Primary ry Literacy Yrs. of Level Level Expecta Immuniza ion Enroll. Enroll. Enroll. Enroll. of Youth Sch. Comp. Comp. ncy tion DPT Measles DALE 1.00 0.63 0.84 0.63 0.55 0.71 0.53 0.60 0.22 0.15 0.21 0.22 Gross Primary Enrollment (125) (125) (114) (97) (98) (73) (73) (73) (124)* (124)*** (124)* (123)* 1.00 0.64 0.83 0.76 0.81 0.51 0.63 0.16 0.17 0.25 0.20 Gross Secondary Enrollment (125) (114) (97) (98) (73) (73) (73) (124)*** (124)*** (124) (123)** 1.00 0.57 0.61 0.80 0.71 0.76 0.17 0.11 0.17 0.23 Net Primary Enrollment (114) (95) (91) (67) (67) (67) (113)*** (113)# (113)*** (113)* 1.00 0.83 0.81 0.55 0.69 0.09 0.17 0.24 0.17 Net Secondary Enrollment (97) (77) (53) (53) (53) (96)# (96)*** (96)* (96)*** 1.00 0.88 0.54 0.75 -0.01 0.21 0.36 0.07 Literacy or Youth (98) (65) (65) (65) (96)# (97)** (97) (96)# 1.00 0.67 0.84 -0.01 0.09 0.29 0.19 Average Years of School (73) (73) (73) (73)# (73)# (73)* (72)*** 1.00 0.70 0.05 0.07 0.20 0.19 First Level Complete (73) (73) (73)# (73)# (73)*** (72)*** 1.00 0.09 0.23 0.36 0.28 Second Level Complete (73) (73)# (73)** (73) (73)* 1.00 0.74 0.66 0.87 Life expectancy at Birth (135) (135) (135) (134) 1.00 0.87 0.73 Immunization DPT (135) (135) (134) 1.00 0.66 Immunization Measles (135) (134) 1.00 DALE (134) Note: 1. Figures are correlation coefficients from Spearman test, number of observations are in parentheses. 2. All coefficients are significant at 1% level, unless indicated otherwise, * 2% significance, ** 5% significance, *** 10% significance, # insignificant 57 Table C.2. Spearman rank-correlation on input efficiency rankings (DEA) Gross Net Gross Seconda Net Seconda Avg. First Second Life Immunizat Primary ry Primary ry Literacy Yrs. of Level Level expecta Immunizat ion Enroll. Enroll. Enroll. Enroll. Youth School Comp. Comp. ncy ion DPT Measles DALE 1.00 0.80 0.88 0.74 0.58 0.70 0.60 0.73 0.30 0.24 0.23 0.30 Gross Primary Enrollment (125) (125) (114) (97) (98) (73) (73) (73) (124) (124) (124) (123) 1.00 0.74 0.94 0.81 0.83 0.65 0.83 0.30 0.29 0.28 0.32 Gross Secondary Enrollment (125) (114) (97) (98) (73) (73) (73) (124) (124) (124) (123) 1.00 0.69 0.64 0.78 0.76 0.80 0.22 0.19 0.17 0.23 Net Primary Enrollment (114) (95) (91) (67) (67) (67) (113)* (113)** (113)*** (113)* 1.00 0.86 0.88 0.75 0.87 0.20 0.24 0.24 0.26 Net Secondary Enrollment (97) (77) (53) (53) (53) (96)** (96)* (96)** (96)* 1.00 0.91 0.73 0.88 0.02 0.18 0.28 0.09 Literacy or Youth (98) (65) (65) (65) (96)# (97)*** (97) (96)# 1.00 0.85 0.97 0.03 0.09 0.24 0.09 Average Years of School (73) (73) (73) (73)# (73)# (73)** (72)# 1.00 0.83 0.14 0.21 0.29 0.18 First Level Complete (73) (73) (73)# (73)*** (73)* (72)# 1.00 0.13 0.21 0.36 0.19 Second Level Complete (73) (73)# (73)*** (73)* (73)# 1.00 0.85 0.77 0.94 Life expectancy at Birth (135) (135) (135) (134) 1.00 0.88 0.89 Immunization DPT (135) (135) (134) 1.00 0.80 Immunization Measles (135) (134) 1.00 DALE (134) Note: 1. Figures are correlation coefficients from Spearman test, number of observations are in parentheses. 2. All coefficients are significant at 1% level, unless indicated otherwise, * 2% significance, ** 5% significance, *** 10% significance, # insignificant 58 Table C.3. Spearman Test on Output Efficiency Rankings (FDH) Gross Net Gross Seconda Net Seconda Avg. First Second Life Immunizat Primary ry Primary ry Literacy Yrs of Level Level expecta Immunizat ion Enroll. Enroll. Enroll. Enroll. of Youth School Comp. Comp. ncy ion DPT Measles DALE 1.00 0.50 0.74 0.34 0.32 0.37 0.44 0.31 0.33 0.23 0.26 0.30 Gross Primary Enrollment (125) (125) (114) (97) (98) (73) (73) (73) (124) (124) (124) (123) 1.00 0.69 0.91 0.85 0.84 0.53 0.79 0.72 0.70 0.84 0.76 Gross Secondary Enrollment (125) (114) (97) (98) (73) (73) (73) (124) (124) (124) (123) 1.00 0.64 0.60 0.66 0.57 0.60 0.63 0.46 0.45 0.59 Net Primary Enrollment (114) (95) (91) (67) (67) (67) (113) (113) (113) (113) 1.00 0.87 0.82 0.33 0.77 0.69 0.73 0.73 0.72 Net Secondary Enrollment (97) (77) (53) (53)* (53) (96) (96) (96) (96) 1.00 0.85 0.56 0.63 0.62 0.67 0.68 0.67 Literacy or Youth (98) (65) (65) (65) (96) (97) (97) (96) 1.00 0.62 0.8 .072 0.73 0.76 0.73 Average Years of School (73) (73) (73) (73) (73) (73) (72) 1.00 0.48 0.49 0.45 0.48 0.56 First Level Complete (73) (73) (73) (73) (73) (72) 1.00 0.75 0.64 0.67 0.78 Second Level Complete (73) (73) (73) (73) (73) 1.00 0.67 0.69 0.94 Life expectancy at Birth (135) (135) (135) (134) 1.00 0.95 0.66 Immunization DPT (135) (135) (134) 1.00 0.70 Immunization Measles (135) (134) 1.00 DALE (134) Note: 1. Figures are correlation coefficients from Spearman test, number of observations are in parentheses. 2. All coefficients are significant at 1% level, unless indicated otherwise, * 2% significance, ** 5% significance, *** 10% significance, # insignificant 59 Table C.4. Spearman Test on Output Efficiency Rankings (DEA) Gross Net Gross Seconda Net Seconda Avg. First Second Life Immunizat Primary ry Primary ry Literacy Years Level Level expecta Immunizat ion Enroll. Enroll. Enroll. Enroll. of Youth School Comp. Comp. ncy ion DPT Measles DALE 1.00 0.48 0.74 0.32 0.30 0.32 0.38 0.25 0.34 0.23 0.27 0.30 Gross Prmary Enrollment (125) (125) (114) (97) (98) (73) (73) (73)** (124) (124) (124) (123) 1.00 0.68 0.95 0.86 0.86 0.52 0.78 0.73 0.73 0.86 0.76 Gross Secondary Enrollment (125) (114) (97) (98) (73) (73) (73) (124) (124) (124) (123) 1.00 0.65 0.61 0.69 0.58 0.62 0.64 0.47 0.45 0.61 Net Primary Enrollment (114) (95) (91) (67) (67) (67) (113) (113) (113) (113) 1.00 0.87 0.83 0.35 0.81 0.69 0.73 0.73 0.72 Net Secondary Enrollment (97) (77) (53) (53) (53) (96) (96) (96) (96) 1.00 0.86 0.56 0.64 0.63 0.66 0.67 0.68 Literacy or Youth (98) (65) (65) (65) (96) (97) (97) (96) 1.00 0.62 0.84 0.73 0.74 0.75 0.73 Average Years of School (73) (73) (73) (73) (73) (73) (72) 1.00 0.46 0.48 0.46 0.48 0.54 First Level Complete (73) (73) (73) (73) (73) (72) 1.00 0.76 0.67 0.66 0.77 Second Level Complete (73) (73) (73) (73) (73) 1.00 0.67 0.69 0.95 Life expectancy at Birth (135) (135) (135) (134) 1.00 0.94 0.67 Immunization DPT (135) (135) (134) 1.00 0.71 Immunization Measles (135) (134) 1.00 DALE (134) Note: 1. Figures are correlation coefficients from Spearman test, number of observations are in parentheses. 2. All coefficients are significant at 1% level, unless indicated otherwise, * 2% significance, ** 5% significance, *** 10% significance, # insignificant 60 Appendix D. Productivity Change Over Time Malmquist indexes are defined using distance functions. These functions describe multiple input-multiple output production technologies based on input and output quantity data without price information or behavioral assumptions (i.e. cost minimization or profit maximization). The distance functions can be either output based or input based. The output distance function can be defined for any production technology St as the reciprocal of the maximum proportional expansion of the output vector y, given inputs x. Do(xt , yt) = inf : (xt , t yt ) St = [sup( :(xt, yt)St) ]-1 (D.1) If (xt, yt) St, then Do 1 and Do= 1 if and only if (xt, yt) is on the boundary or frontier of technology. The distance function is the reciprocal of the output efficiency measure defined by Farrell and used in previous sections. In Figure D.1, the frontier of the transformation set is defined by (Bt, Ct) in period t and by (Bt+1, Ct+1) in period t+1. The distance of country A from the country B in period t, which is a measure of how far the production point A is from the frontier, can be expressed as Dt (xt , yt ) = OAt /OBt . Similarly, the distance between the production point At+1 and the frontier in period t+1 is defined as Dt+1(xt+1, yt+1) = OAt /OBt . +1 +1 Y2 Bt+1 Bt At+1 At Ct+1 Ct O Y1 Figure D. 1. Output Possibility Set, periods t and t+1 The Malmquist index requires the definition of a distance function with respect to two different time periods (t and t+1). This distance measures the maximum change in outputs required to make (xt+1, yt+1) feasible in relation to technology at t, and is defined as Dt (xt , yt ) = OAt /OBt . Alternatively, the distance function could be defined as +1 +1 +1 61 the change in output required to make (xt, yt) feasible in relation to technology at t+1. This would be defined as Dt+1(xt , yt ) = OAt /OBt . Hence the Malmquist productivity +1 index is defined as the ratio of two distances, that can be computed in relation with technology at t or at t+1. The period t -based and period (t+1)-based Malmquist indices are defined, respectively, as M0 = t Dt (xt+1, yt+1) (D.2) Dt (xt , yt ) M0 = t Dt+1(xt+1, yt+1) (D.3) Dt (xt , yt ) +1 One possible case in reality is that the frontier shift is not parallel in all dimensions, as indicated in Figure D.2. Country B in period t+1 is producing more y1 and less y2 compared to the production point in period t. In another word, the country B is not expanding along the same ray through the origin, but rather biased in some direction, as pointed by Nin, Arndt, and Preckel (2003) among others. In this case, the output-oriented, period t-based Malmquist index will estimate productivity decrease due to technical regress while the period (t+1)-based Malmquist will show the opposite. Y2 Bt Bt+1 O Y1 Figure D. 2 Contemporaneous Production Set (Biased Technical Change) To avoid an arbitrary selection of base period mentioned above, the geometric average of both is suggested (Fare, et al, 1994): 62 Mo( xt+1, yt+1 , xt, yt) = Dt(xt+1, yt+1)Dt+1( xt+1,yt+1) 12 (D.4) Dt ( xt,yt) Dt+1( xt, yt) This expression can be rewritten as: Dt+1 xt+1 ( , yt+1) 12 Mo( xt+1, yt+1 , xt, yt) = Dt ( xt+1,yt+1) Dt ( xt,yt) Dt(xt, yt) Dt+1(xt+1, yt+1) Dt+1(xt, yt) (D.5) The ratio outside the brackets captures the change in relative efficiency between the two time periods. The term in the brackets captures the technological shift between the two periods. This expression is the basis of our empirical application, following Coelli and Rao (2003). An alternative approach to dealing with the biased technical change is to define a sequential production set, following Nin, Arndt, and Preckel (2003). Specifically, it is assumed that the input-output mix, or technology, in period t is always available in period t+1. The production possibility set, the sequential one, in period t+1 is then defined by the frontier (Bt, Bt+1) in Figure D.3. This setup will clearly rule out the possibility of technical regress and give lower efficiency change than otherwise. Y2 Bt Bt+1 O Y1 Figure D. 3 Sequential Production Set (Biased Technical Change) 63 Variable Returns to Scale Efficiency and Sequential Technical Change Table D.1. Education, single input (public spending per capita on education), single output Region VRSTE Output VRSTE Input EFFCH TECHCH TFPCH No. of 1975-80 1996-02 1975-80 1996-02 Countries Gross AFR .563 .650 .843 .851 1.299 1 1.299 23 Primary EAP .793 .808 .897 .847 .987 1 .987 8 Enrollment ECA .754 .735 .845 .793 .944 1 .944 4 LAC .787 .813 .860 .843 1.054 1 1.054 20 MNA .694 .692 .798 .747 1.114 1 1.114 10 SAS .554 .769 .882 .911 1.446 1 1.446 5 Net Primary AFR .537 .651 .841 .819 1.355 1 1.355 12 Enrollment EAP .929 .959 .927 .859 .969 1 .969 4 ECA .958 .907 .792 .799 .963 1 .963 2 LAC .870 .935 .837 .831 1.045 1 1.045 13 MNA .752 .842 .787 .724 1.198 1 1.198 9 SAS - - - - - - - - Gross AFR .184 .293 .819 .830 2.072 1.038 2.150 23 Secondary EAP .508 .705 .874 .860 1.484 1.038 1.540 8 Enrollment ECA .750 .864 .913 .854 1.235 1.038 1.281 4 LAC .564 .723 .859 .874 1.450 1.038 1.505 20 MNA .521 .703 .804 .774 2.443 1.038 2.535 10 SAS .324 .478 .880 .901 1.806 1.038 1.874 5 Net AFR .179 .341 .317 .304 1.519 1.248 1.895 6 Secondary EAP .576 .695 .525 .623 1.555 1.248 1.941 3 Enrollment ECA .824 .895 .747 .711 1.256 1.248 1.568 1 LAC .535 .678 .504 .451 1.420 1.248 1.772 10 MNA .385 .629 .453 .410 1.891 1.248 2.360 8 SAS - - - - - - - - Literacy of AFR .554 .741 .814 .831 1.442 1 1.442 20 Youth EAP .924 .988 .879 .868 1.009 1 1.009 6 ECA .967 .990 .940 .880 .967 1 .967 4 LAC .899 .952 .872 .845 1.024 1 1.024 18 MNA .729 .906 .778 .749 1.230 1 1.230 10 SAS .499 .662 .869 .871 1.430 1 1.430 5 Average AFR .261 .323 .340 .315 1.737 1 1.737 19 Years of EAP .653 .708 .406 .495 1.342 1 1.342 7 School ECA .750 .768 .648 .621 1.387 1 1.387 3 LAC .618 .625 .418 .427 1.300 1 1.300 18 MNA .456 .549 .389 .326 1.929 1 1.929 6 SAS .302 .397 .363 .379 2.137 1 2.137 5 First Level AFR .135 .164 .340 .315 1.417 1 1.417 19 Complete EAP .367 .382 .363 .342 1.066 1 1.066 7 ECA .764 .639 .646 .528 .913 1 .913 3 LAC .372 .266 .404 .349 .816 1 .816 18 MNA .299 .217 .389 .317 1.266 1 1.266 6 SAS .146 .194 .363 .370 2.101 1 2.101 5 Second AFR .082 .098 .341 .339 1.417 1.77 2.509 19 Level EAP .439 .444 .470 .517 .991 1.77 1.754 7 Complete ECA .284 .276 .355 .414 1.045 1.77 1.849 3 LAC .337 .228 .418 .381 .839 1.77 1.485 18 MNA .357 .266 .389 .357 1.233 1.77 2.182 6 SAS .202 .235 .385 .424 1.734 1.77 3.068 5 64 Table D.2 Health, Single Input (Public Spending per capita on Health), Single Output Region VRSTE Output VRSTE Input EFFCH TECHCH TFPCH No. of 1997-99 2000-02 1997-99 2000-02 Countries Life AFR .642 .618 .680 .681 .972 1 .972 42 Expectancy EAP .870 .872 .738 .735 1.008 1 1.008 16 at Birth ECA .919 .911 .616 .626 1.019 1 1.019 25 LAC .923 .920 .739 .723 .995 1 .995 31 MNA .889 .892 .725 .754 1.049 1 1.049 13 SAS .821 .834 .713 .718 1.029 1 1.029 5 Immunization AFR .601 .629 .686 .682 1.022 1.078 1.101 42 DPT EAP .837 .824 .772 .740 .930 1.078 1.003 16 ECA .949 .957 .681 .633 .953 1.078 1.027 25 LAC .863 .883 .732 .694 .944 1.078 1.017 31 MNA .882 .920 .778 .751 1.063 1.078 1.146 13 SAS .742 .773 .736 .724 .976 1.078 1.053 5 Immunization AFR .632 .638 .682 .681 .975 1.089 1.061 42 Measles EAP .837 .827 .778 .740 .924 1.089 1.007 16 ECA .944 .951 .712 .634 .943 1.089 1.027 25 LAC .904 .912 .770 .694 .924 1.089 1.006 31 MNA .878 .909 .798 .755 1.055 1.089 1.148 13 SAS .701 .732 .735 .725 .970 1.089 1.056 5 DALE AFR .655 - .563 - - - - 41 EAP .717 - .830 - - - - 16 ECA .602 - .903 - - - - 26 LAC .698 - .904 - - - - 31 MNA .707 - .863 - - - - 15 SAS .691 - .787 - - - - 5 65 Table D.3. Education, Multiple Inputs, Multiple Outputs Region VRSTE Output VRSTE Input EFFCH TECHCH TFPCH No. of 1975-80 1996-02 1975-80 1996-02 Countries EDU2-2 AFR .587 .685 .906 .902 1.292 1.003 1.296 21 Gross EAP .860 .928 .935 .905 1.039 1.030 1.070 7 Primary and ECA .913 .939 .913 .842 .937 1.065 .999 3 Secondary LAC .854 .911 .906 .914 1.102 1.029 1.134 20 Enrollment MNA .729 .820 .841 .793 1.278 1.029 1.314 10 SAS .580 .817 .940 .963 1.457 1.101 1.470 5 EDU2-2n AFR .723 .703 .787 .750 1.062 1.009 1.076 6 Net Primary EAP .921 .954 .905 .881 1.015 1.074 1.088 3 and ECA 1.00 .973 1.00 .836 .999 1.299 1.298 1 Secondary LAC .881 .942 .808 .822 1.074 1.066 1.138 9 Enrollment MNA .782 .862 .777 .695 1.168 1.097 1.286 8 SAS - - - - - - - - EDU3-2 AFR .762 .922 .909 .909 1.043 1.002 1.045 18 Gross EAP .840 .929 .896 .896 1.066 1.022 1.089 6 Primary and ECA .913 .917 .909 .909 1.018 1.037 1.057 3 Secondary LAC .849 .919 .922 .922 1.116 1.021 1.139 18 Enrollment MNA .787 .870 .892 .892 1.235 1.008 1.245 10 SAS .813 .966 .982 .982 1.140 1.010 1.153 5 EDU3-2n AFR .909 .894 .924 .897 .953 1.014 .970 6 Net Primary EAP .937 .981 .961 .959 1.030 1.021 1.052 2 and ECA 1.00 .996 1.00 .969 .916 1.300 1.192 1 Secondary LAC .964 .983 .931 .948 1.045 1.063 1.109 9 Enrollment MNA .930 .950 .934 .947 1.137 1.078 1.225 8 SAS - - - - - - - - EDU3-3 AFR .939 .946 .950 .944 .974 1.018 .991 18 Gross EAP .995 .996 .989 .968 .961 1.026 .986 6 Primary & ECA .999 1.00 .993 .996 .959 1.029 .987 3 Secondary LAC .968 .983 .966 .960 .996 1.023 1.019 18 Enrollment, MNA .959 .966 .964 .953 .956 1.008 .965 10 Literacy of SAS .919 .930 .970 .983 1.027 1.007 1.036 5 Youth EDU3-3bl AFR .789 .724 .896 .876 1.025 1.167 1.201 15 Avg. Yrs. of EAP .902 .872 .942 .901 .989 1.279 1.256 6 School, First ECA .957 .987 .962 .978 1.026 1.137 1.168 2 & Secondary LAC .893 .846 .939 .883 .999 1.170 1.168 17 Level MNA .899 .811 .925 .827 .950 1.259 1.193 6 Complete SAS .883 .888 .984 .956 1.129 1.375 1.547 5 EDU2-3bl AFR .416 .451 .725 .733 1.560 1.054 1.641 17 Avg. Yrs. of EAP .730 .778 .747 .732 1.064 1.106 1.178 7 School, First ECA .938 .943 .873 .773 .885 1.047 .922 2 & Secondary LAC .690 .690 .777 .713 1.070 1.072 1.146 18 Level MNA .496 .576 .661 .599 1.393 1.105 1.509 6 Complete SAS .328 .510 .673 .808 2.189 1.086 2.378 5 66 Table D.4. Health, Multiple Inputs and Multiple Outputs Region VRSTE Output VRSTE Input EFFCH TECHCH TFPCH No. of 1997-99 2000-02 1997-99 2000-02 Countries HEA2-2 Life AFR .818 .802 .861 .842 .952 1.032 .982 31 Expectancy EAP .899 .897 .853 .818 .950 1.055 1.001 9 at birth, ECA .966 .965 .755 .730 .954 1.063 1.014 18 Immunization LAC .941 .936 .843 .824 .950 1.051 .998 23 DPT MNA .973 .970 .915 .902 .983 1.041 1.023 11 SAS .957 .956 .939 .907 .965 1.032 .995 4 HEA3-2 Life AFR .823 .805 .866 .842 .952 1.031 .982 31 Expectancy EAP .904 .903 .853 .818 .950 1.054 1.001 9 at birth, ECA .970 .969 .763 .736 .957 1.059 1.013 18 Immunization LAC .948 .943 .862 .838 .950 1.051 .998 23 DPT MNA .973 .970 .907 .893 .984 1.060 1.044 10 SAS .957 .957 .939 .907 .970 1.031 .999 4 HEA3-2 Life AFR .820 .787 .866 .838 .934 1.029 .961 31 Expectancy EAP .900 .898 .860 .817 .937 1.069 1.001 9 at birth, ECA .971 .970 .798 .739 .942 1.078 1.015 18 Immunization LAC .957 .953 .887 .848 .941 1.062 .998 23 Measles MNA .972 .971 .908 .894 .986 1.064 1.050 10 SAS .952 .957 .937 .906 .962 1.046 1.005 4 HEA3-3 Life AFR .830 .812 .868 .842 .952 1.031 .981 31 Expectancy EAP .904 .903 .860 .819 .941 1.064 1.001 9 at birth, ECA .977 .974 .800 .740 .944 1.075 1.013 18 Immunization LAC .958 .954 .887 .848 .941 1.062 .998 23 DPT & MNA .974 .971 .909 .895 .986 1.063 1.049 10 Measles SAS .958 .957 .941 .907 .965 1.039 1.001 4 wb176149 C:\ddrive\Public Expenditure\Efficiency of Public Spending in Developing Countries_MAR05.doc March 4, 2005 4:21 PM 67